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1
蕭德權 and Tak-kuen Siu. "Risk measures in finance and insurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242297.
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2
Gong, Qi, and 龔綺. "Gerber-Shiu function in threshold insurance risk models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40987966.
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3
Wan, Lai-mei. "Ruin analysis of correlated aggregate claims models." Thesis, Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B30705708.
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4
Chau, Ki-wai, and 周麒偉. "Fourier-cosine method for insurance risk theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/208586.
Testo completoAbstract (sommario):
In this thesis, a systematic study is carried out for effectively approximating Gerber-Shiu functions under L´evy subordinator models. It is a hardly touched topic in the recent literature and our approach is via the popular Fourier-cosine method.
In theory, classical Gerber-Shiu functions can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. Therefore, an efficient numerical method based on Fourier transform is pursued in this thesis for evaluating Gerber-Shiu functions.
Fourier-cosine method is a numerical method based on Fourier transform and has been very popular in option pricing since its introduction. It then evolves into a number of extensions, and we here adopt its spirit to insurance risk theory. In this thesis, the proposed approximant of Gerber-Shiu functions under an L´evy subordinator model has O(n) computational complexity in comparison with that of O(n log n) via the usual numerical Fourier inversion. Also, for Gerber-Shiu functions within the proposed refined Sobolev space, an explicit error bound is given and error bound of this type is seemingly absent in the literature.
Furthermore, the error bound for our estimation can be further enhanced under extra assumptions, which are not immediate from Fang and Oosterlee’s works. We also suggest a robust method on the estimation of ruin probabilities (one special class of Gerber-Shiu functions) based on the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the use of our Fourier-cosine method in ruin probability, resulting in an effective global estimation. Finally, the effectiveness of our result will be further illustrated in a number of numerical studies and our enhanced error bound is apparently optimal in our demonstration; more precisely, empirical evidence exhibiting the biggest possible error convergence rate agrees with our theoretical conclusion.<br>published_or_final_version<br>Mathematics<br>Master<br>Master of Philosophy
5
Kwan, Kwok-man, and 關國文. "Ruin theory under a threshold insurance risk model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B38320034.
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Liu, Luyin, and 劉綠茵. "Analysis of some risk processes in ruin theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195992.
Testo completoAbstract (sommario):
In the literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multi-dimensional risk and dependent structures respectively.
The first one is a bivariate risk process with a dividend barrier, which concerns a two-dimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process.
The second risk process is a semi-Markovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the Gerber-Shiu expected discounted penalty function that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time before ruin are given along with some numerical examples.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Master<br>Master of Philosophy
7
Chen, Yiqing, and 陳宜清. "Study on insurance risk models with subexponential tails and dependence structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841768.
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Lin, Erlu, and 林尔路. "Analysis of dividend payments for insurance risk models with correlated aggregate claims." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203992.
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Wong, Tsun-yu Jeff, and 黃峻儒. "On some Parisian problems in ruin theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206448.
Testo completoAbstract (sommario):
Traditionally, in the context of ruin theory, most judgements are made on an immediate sense. An example would be the determination of ruin, in which a business is declared broke right away when it attains a negative surplus. Another example would be the decision on dividend payment, in which a business pays dividends whenever the surplus level overshoots certain threshold. Such scheme of decision making is generally being criticized as unrealistic from a practical point of view. The Parisian concept is therefore invoked to handle this issue. This idea is deemed more realistic since it allows certain delay in the execution of decisions. In this thesis, such Parisian concept is utilized on two different aspects.
The first one is to incorporate this concept on defining ruin, leading to the introduction of Parisian ruin time. Under such a setting, a business is considered ruined only when the surplus level stays negative continuously for a prescribed length of time. The case for a fixed delay is considered. Both the renewal risk model and the dual renewal risk model are studied. Under a mild distributional assumption that either the inter arrival time or the claim size is exponentially distributed (while keeping the other arbitrary), the Laplace transform to the Parisian ruin time is derived. Numerical example is performed to confirm the reasonableness of the results. The methodology in obtaining the Laplace transform to the Parisian ruin time is also demonstrated to be useful in deriving the joint distribution to the number of negative surplus causing or without causing Parisian ruin.
The second contribution is to incorporate this concept on the decision for dividend payment. Specifically, a business only pays lump-sum dividends when the surplus level stays above certain threshold continuously for a prescribed length of time. The case for a fixed and an Erlang(n) delay are considered. The dual compound Poisson risk model is studied. Laplace transform to the ordinary ruin time is derived. Numerical examples are performed to illustrate the results.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Master<br>Master of Philosophy
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Zhu, Jinxia, and 朱金霞. "Ruin theory under Markovian regime-switching risk models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203980.
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Leboho, Nakedi Wilson. "Quantitative Risk Management and Pricing for Equity Based Insurance Guarantees." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96980.
Testo completoAbstract (sommario):
Thesis (MSc)--Stellenbosch University, 2015<br>ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed annuities, whereby investors participate in the security markets through insurance companies that guarantee them a minimum of their invested premiums. The difference between
the financial options and options embedded in equity-based policies is that financial ones are financed by the option buyers’ premiums, whereas options of the equity-based policies are financed by also continuous fees that follow
the premium paid first by the policyholders during the life of the contracts. Other important dissimilarities are that equity-based policies do not give the owner the right to sell the contract, and carry not just security market related
risk, but also insurance related risks such as the selection rate, behavioural, mortality, others and the systematic longevity. Thus equity-based annuities are much complicated insurance products to precisely value and hedge. For insurance companies to successfully fulfil their promise of eventually returning at least initially invested amount to the policyholders, they have to be able to
measure and manage risks within the equity-based policies. So in this thesis, we do fair pricing of the variable and equity indexed annuities, then discuss management of financial market and insurance risks management.<br>AFRIKAANSE OPSOMMING : Aandeel-gebaseerde versekering waarborg ook bekend as eenheid-gekoppelde annuiteite is eksotiese, langtermyn-en pad-afhanklike opsies wat in veranderlike en gelykheid geindekseer annuiteite, waardeur beleggers neem in die sekuriteit markte deur middel van versekering maatskappye wat waarborg hulle ’n minimum
van geklassifiseer kan word hulle belˆe premies. Die verskil tussen die finansi¨ele opsies en opsies is ingesluit in aandele-gebaseerde beleid is dat die finansi¨ele mense is gefinansier deur die opsie kopers se premies, terwyl opsies van die aandele-gebaseerde beleid word deur ook deurlopende fooie wat volg op die premie wat betaal word eers deur die polishouers gefinansier gedurende die lewe van die kontrakte. Ander belangrike verskille is dat aandele-gebaseerde beleid gee nie die eienaar die reg om die kontrak te verkoop, en dra nie net markverwante risiko sekuriteit, maar ook versekering risiko’s, soos die seleksie
koers, gedrags, sterftes, ander en die sistematiese langslewendheid. So aandeel-gebaseerde annuiteite baie ingewikkeld versekering produkte om presies waarde en heining. Vir versekeringsmaatskappye suksesvol te vervul hul
belofte van uiteindelik ten minste aanvanklik belˆe bedrag terug te keer na die polishouers, hulle moet in staat wees om te meet en te bestuur risiko’s binne die aandeel-gebaseerde beleid. So in hierdie tesis, ons doen billike pryse van die veranderlike en gelykheid geïndekseer annuiteite, bespreek dan die bestuur van finansiele markte en versekering risiko’s bestuur.
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Yeo, Keng Leong Actuarial Studies Australian School of Business UNSW. "Claim dependence in credibility models." Awarded by:University of New South Wales. School of Actuarial Studies, 2006. http://handle.unsw.edu.au/1959.4/25971.
Testo completoAbstract (sommario):
Existing credibility models have mostly allowed for one source of claim dependence only, that across time for an individual insured risk or a group of homogeneous insured risks. Numerous circumstances demonstrate that this may be inadequate and insufficient. In this dissertation, we developed a two-level common effects model, based loosely on the Bayesian model, which allows for two possible sources of dependence, that across time for the same individual risk and that between risks. For the case of Normal common effects, we are able to derive explicit formulas for the credibility premium. This takes the intuitive form of a weighted average between the individual risk's claims experience, the group's claims experience and the prior mean. We also consider the use of copulas, a tool widely used in other areas of work involving dependence, in constructing credibility premiums. Specifically, we utilise copulas to model the dependence across time for an individual risk or group of homogeneous risks. We develop the construction with several well-known families of copulas and are able to derive explicit formulas for their respective conditional expectations. Whilst some recent work has been done on constructing credibility models with copulas, explicit formulas for the conditional expectations have rarely been made available. Finally, we calibrate these copula credibility models using a real data set. This data set relates to the claims experience of workers' compensation insurance by occupation over a 7-year period for a particular state in the United States. Our results show that for each occupation, claims dependence across time is indeed present. Amongst the copulas considered in our empirical analysis, the Cook-Johnson copula model is found to be the best fit for the data set used. The calibrated copula models are then used for prediction of the next period's claims. We found that the Cook-Johnson copula model gives superior predictions. Furthermore, this calibration exercise allowed us to uncover the importance of examining the nature of the data and comparing it with the characteristics of the copulas we are calibrating to.
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Maj, Mateusz. "Essays in risk management: conditional expectation with applications in finance and insurance." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209668.
Testo completoAbstract (sommario):
In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Zhou, Junhua, and 周俊华. "To survive and succeed in the risky financial world: applications of mathematical optimization in finance andinsurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44407579.
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Ndoumbe, Ebongue Steve Armand. "The risk model for insurance portfolio has been adopted to portfolio of derivatives. Describe the models and compare with a focus on the differences." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-11293.
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Drakenward, Ellinor, and Emelie Zhao. "Modeling risk and price of all risk insurances with General Linear Models." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-275696.
Testo completoAbstract (sommario):
Denna kandidatexamen ligger inom området matematisk statistik. I samarbete med försäkringsbolaget Hedvig syftar denna avhandling till att utforska en ny metod för hantering av Hedvigs försäkringsdata genom att bygga en prissättningsmodell för alla riskförsäkringar med generaliserade linjära modeller. Två generaliserade linjära modeller byggdes, där den första förutspår frekvensen för ett anspråk och den andra förutspår svårighetsgraden. De ursprungliga uppgifterna delades in i 9 förklarande variabler. Båda modellerna inkluderade fem förklarande variabler i början och reducerades sedan. Minskningen resulterade i att fyra av fem egenskaper var förklarande signifikanta i frekvensmodellen och endast en av de fem var förklarande signifikanta i svårighetsmodellen. Var och en av modellerna erhöll relativa risker för nivåerna av deras förklarande variabler. De relativa riskerna resulterade i en total risk för varje nivå. Genom multiplicering av en skapad basnivå med en uppsättning kombination av riskparametrar kan premien för en vald kund erhållas.<br>Det här kandidatexamensarbetet ligger inom ämnet matematisk statistik. Jag samarbete med försäkringsbolaget Hedvig, avser uppsatsen att undersöka en ny metod att hantera Hedvigs försäkringsdata genom att bygga en prissättningsmodell för drulleförsäkring med hjälp av generaliserade linjära modeller. Två modeller skapades varav den första förutsättningen frekvensen av ett försäkringsanspråk och den andra förutsäger storleken. Originaldatan var indelad i 9 förklarande variabler. Båda modellerna innehöll till en början fem förklarande variabler, vilka sedan reducerades till fyra respektive en variabler i de motsvarande modellerna. Från varje modell kunde sedan de relativa riskerna tas fram för varje kategori av de förklarande variablerna. Tillsammans bildades sedan totalrisken för alla grupper.
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Badran, Rabih. "Insurance portfolio's with dependent risks." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209547.
Testo completoAbstract (sommario):
Cette thèse traite de portefeuilles d’assurance avec risques dépendants en théorie du risque.<p>Le premier chapitre traite les modèles avec risques équicorrelés. Nous proposons une structure mathématique qui amène à une fonction génératrice de probabilités particulière (fgp) proposé par Tallis. Cette fgp implique des variables équicorrelées. Puis, nous étudions l’effet de ce type de dépendance sur des quantités d’intérêt dans la littérature actuarielle telle que la fonction de répartition de la somme des montants des sinistres, les primes stop-loss et les probabilités de ruine sur horizon fini. Nous utilisons la structure proposée pour corriger des erreurs dans la littérature dues au fait que plusieurs auteurs agissaient comme si la somme des variables aléatoires équicorrélés aient nécessairement la fgp proposée par Tallis. <p><p>Dans le second chapitre, nous proposons un modèle qui combine les modèles avec chocs et les modèles avec mélanges communs en introduisant une variable qui contrôle le niveau du choc. Dans le cadre de ce nouveau modèle, nous considérons deux applications où nous généralisons le modèle de Bernoulli avec choc et le modèle de Poisson avec choc. Nous étudions, dans les deux applications, l’effet de la dépendance sur la fonction de répartition des montants des sinistres, les primes stop-loss et les probabilités de ruine sur horizon fini et infini. Pour la deuxième application, nous proposons une construction basée sur les copules qui permet de contrôler le niveau de dépendance avec le niveau du choc.<p><p>Dans le troisième chapitre, nous proposons, une généralisation du modèle classique de Poisson où les montants des sinistres et les intersinistres sont supposés dépendants. Nous calculons la transformée de Laplace des probabilités de survie. Dans le cas particulier où les montants des sinistres ont une distribution exponentielle nous obtenons des formules explicites pour les probabilités de survie. <p><p>Dans le quatrième chapitre nous généralisons le modèle classique de Poisson en introduisant de la dépendance entre les intersinistres. Nous utilisons le lien entre les files fluides et le processus du risque pour modéliser la dépendance. Nous calculons les probabilités de survie en utilisant un algorithme numérique et nous traitons le cas où les montants de<p>sinistres et les intersinistres ont des distributions de type phase.<p><br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Yamazato, Makoto. "Non-life Insurance Mathematics." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96535.
Testo completoAbstract (sommario):
In this work we describe the basic facts of non-life insurance and then explain risk processes. In particular, we will explain in detail the asymptotic behavior of the probability that an insurance product may end up in ruin during its lifetime. As expected, the behavior of such asymptotic probability will be highly dependent on the tail distribution of each claim.<br>En este artículo describimos los conceptos básicos relacionados a seguros que no sean de vida y luego explicamos procesos de riesgo. En particular, tratamos al detalle el comportamiento asintótico de la probabilidad de que un producto sea declarado en ruina. Como es suponible, el comportamiento en el horizonte depende de la cola de la distribución de las primas.
19
Gathy, Maude. "On some damage processes in risk and epidemic theories." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210063.
Testo completoAbstract (sommario):
Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique.<p><p>En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance.<p><p>Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya.<p><p>Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique. <p><p>Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives.<p><p>Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées. <p><p><p><br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Sahlin, Carl, and Carl-Johan Hugner. "Dealing with the ORSA : A Dynamic Risk-Factor Based Approach for the Small, Swedish Non-Life Insurer." Thesis, KTH, Industriell Management, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133477.
Testo completoAbstract (sommario):
The Own Risk and Solvency Assessment, ORSA, is referred to as the heart of the regulation to be for European insurance companies - Solvency II. The aim of the ORSA process is to provide an overall and holistic view of the insurer’s risks by analyzing their current financial status and business strategy at hand. There is no predefined way to implement this process, which means that the companies are forced to develop a model themselves, as they see fit. In collaboration with a regional insurance company in Sweden we develop a structure and framework for an ORSA-model, flexible enough to be used by similar insurers yet standardized enough to overcome the issue of constrained resources within these smaller organizations. We apply a risk-factor based approach and tie together a balance sheet projection and stress testing, designed to be further developed as the individual insurer see fit. The suggested approach yields partially satisfying results and we consider the model to be particularly well-suited for assessing risk in the context of the small, non-life insurer.<br>Den egna risk- och solvensutvärderingen, ORSA, kallas hjärtat av det kommande regelverket för europeiska försäkringsbolag - Solvens II. Syftet med ORSA-processen är att ge en övergripande helhetsbild av försäkringsgivarens risker genom att analysera deras finansiella ställning och affärsstrategi. Det finns inget fördefinierat sätt att genomföra denna process, vilket innebär att företagen tvingas att utveckla en modell på egen hand, på ett sätt som de finner lämpligt. I samarbete med ett regionalt försäkringsbolag i Sverige utvecklar vi en struktur och en grund för en ORSA-modell. En modell som är tillräckligt flexibel för att kunna användas av liknande försäkringsgivare men samtidigt standardiserad nog att lösa problemet med begränsade resurser i dessa mindre organisationer. Vi tillämpar en riskfaktor-baserad metod, prognostiserar resultat- och balansräkning för bolaget och utför stresstester. Metoden är utformad för att utvecklas vidare av den enskilde försäkringsgivaren så som de finner lämpligt. Den föreslagna metoden ger delvis tillfredsställande resultat och vi anser att det är en grund väl lämpad att använda som utgångspunkt för att konstruera riskmätningsmetoder för små, skadeförsäkringsbolag.
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Gong, Qi. "Gerber-Shiu function in threshold insurance risk models." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40987966.
Testo completo
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Solcà, Tatiana. "Expected risk-adjusted return for insurance based models." Zürich : Swiss Federal Institute of Technology Zurich, Department of Mathematics, 2000. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=21.
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Wat, Kam-pui, and 屈錦培. "Discrete-time insurance risk models with dependence structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B47849666.
Testo completoAbstract (sommario):
Regarding the relationships among different insurance claims, especially in
non-life insurance, the dependence behaviour in various models has been studied
extensively. In this thesis, some discrete-time risk models with dependence
structures would be investigated.
One traditional discrete-time risk model is the time series risk model, in
which the dependence would be on two aspects: time correlated claims and dependent
business classes. A general vector (multivariate) autoregressive moving
average (VARMA) model would be adopted to analyze the ruin probability
of a surplus process. An upper bound for the ruin probability is derived for the
general order of multivariate time series models in claims. Simulation studies
are carried out for model comparison for finite time ruin probabilities.
Another class of risk model is the compound binomial risk model, where the
dependence structure would be based on the existence of a so-called by-claim
in the claim process. The by-claim could be incurred in the same period as the
main insurance claim, or it would be incurred in the next period, depending
on a certain probability. A randomized dividend payment scheme with some
fixed threshold value in surplus level would also be considered in this thesis. A
methodology is discovered to obtain the Gerber-Shiu expected penalty function
for the extended model.
The final model investigated in this thesis is the periodic time series risk
model. The periodic structure of the model gives a practical interpretation
of the business cycle, in which there are high season and low season for the
business. Some lower order periodic time series models are considered for the
claim structures.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
24
Siu, Kin-bong Bonny, and 蕭健邦. "Expected shortfall and value-at-risk under a model with market risk and credit risk." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37727473.
Testo completo
25
Ngwenza, Dumisani. "Quantifying Model Risk in Option Pricing and Value-at-Risk Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31059.
Testo completoAbstract (sommario):
Financial practitioners use models in order to price, hedge and measure risk. These models are reliant on assumptions and are prone to ”model risk”. Increased innovation in complex financial products has lead to increased risk exposure and has spurred research into understanding model risk and its underlying factors. This dissertation quantifies model risk inherent in Value-at-Risk (VaR) on a variety of portfolios comprised of European options written on the ALSI futures index across various maturities. The European options under consideration will be modelled using the Black-Scholes, Heston and Variance-Gamma models.
26
Ong, Alen Sen Kay. "Asset location decision models in life insurance." Thesis, City University London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336430.
Testo completo
27
Wu, Xueyuan, and 吳學淖. "On insurance risk models with correlated classes of business." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B27575329.
Testo completoAbstract (sommario):
(Uncorrected OCR)
Abstract of the thesis entitled
ON INSURANCE RISK MODELS WITH CORRELATED CLASSES OF BUSINESS
submitted by Wu Xueyuan
for the degree of Doctor of Philosophy
at The University of Hong Kong in February 2004
In this thesis, we focus on ruin analysis of risk models wIth correlated classes of insurance business. Specifically, five risk models with different dependence relations between classes are introduced. For these models, various problems related to ruin probability are considered.
vVe first study a continuous-time correlated aggregate clmms model with Poisson and Erlang risk processes. In this model, we assume that two classes of business are correlated through a common Erlang component in thelf claim-number processes. We derive an explicit expression for the mfimte-time survival probability of the assumed model when claim SIzes are exponentially distributed. For general claim-size distributions, we obtain some result for the infinite-time ruin
probabIlIty, and present a numerical method for evaluating the probability of
rum.
Based on the continuous-tIme model of Yuen and "Vang (2002) with thin-
ning correlatIOn, we propose a new dependence relatIOn with interaction between classes of business in the discrete-time case. Two dIscrete-time risk models with such a relation of dependence are studied. For the first interaction model: we investIgate the statIstical properties of the aggregate claIms for a family of claimnumber distributions. \Ve also compare the model with other existing models with correlated aggregate claIms in terms of the finite-time and infimte-time ruin probabllitles. The second model extends the interaction dependence to the case of the compound binomlal model with delayed claims. For this model, we develop a recursive method to compute the finite-time survival probabilities: and derive an explicit expression for the infinite-time survival probability in a special case.
The last two risk models proposed in this thesis are the bivariate compound binomial model and the bivariate compound Poisson model. In the bivariate case: vanous definitions of ruin can be considered. For the bivariate compound binomial model, recursive algorithms for calculating several kinds of finite-time survival probability are presented and numerical examples are given. As for the bivariate compound Poisson model, we study the probabllity that at least one of the two classes of business will get ruined. Since this bivanate ruin probability is very dlfficult to deal with, we use the result of the bivariate compound binomial model to approximate the desired bivanate finite-time survlval probability. \Ve also obtain an upper bound for the infinite-time ruin probability via some association properties of the model. For a simplified version of the model, we examine
'l'l
the mfimte-time ruin probability when claIm sizes are exponentially distributed.<br>abstract<br>toc<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
28
Gu, Jiawen, and 古嘉雯. "On credit risk modeling and credit derivatives pricing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/202367.
Testo completoAbstract (sommario):
In this thesis, efforts are devoted to the stochastic modeling, measurement and evaluation of credit risks, the development of mathematical and statistical tools to estimate and predict these risks, and methods for solving the significant computational problems arising in this context.
The reduced-form intensity based credit risk models are studied. A new type of reduced-form intensity-based model is introduced, which can incorporate the impacts of both observable trigger events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. In addition, this thesis focuses on the relationship between structural firm value model and reduced-form intensity based model. A continuous time structural asset value model for the asset value of two correlated firms with a two-dimensional Brownian motion is studied. With the incomplete information introduced, the information set available to the market participants includes the default time of each firm and the periodic asset value reports. The original structural model is first transformed into a reduced-form model. Then the conditional distribution of the default time as well as the asset value of each name are derived. The existence of the intensity processes of default times is proven and explicit form of intensity processes is given in this thesis.
Discrete-time Markovian models in credit crisis are considered. Markovian models are proposed to capture the default correlation in a multi-sector economy. The main idea is to describe the infection (defaults) in various sectors by using an epidemic model. Green’s model, an epidemic model, is applied to characterize the infectious effect in each sector and dependence structures among various sectors are also proposed. The models are then applied to the computation of Crisis Value-at-Risk (CVaR) and Crisis Expected Shortfall (CES). The relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults is investigated using the Probabilistic Boolean Network (PBN). The idea is to model the credit default process by a PBN and the network structure can be inferred by using Markov chain theory and real-world data.
A reduced-form model for economic and recorded default times is proposed and the probability distributions of these two default times are derived. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data. A simple and efficient method, based on the ordered default rate, is derived to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. Analytical expressions for the ordered default time distributions with recursive formulas for the coefficients are given, which makes the calculation fast and efficient in finding rates of basket CDSs.<br>published_or_final_version<br>Mathematics<br>Doctoral<br>Doctor of Philosophy
29
Liu, Binbin, and 刘彬彬. "Some topics in risk theory and optimal capital allocation problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48199291.
Testo completoAbstract (sommario):
In recent years, the Markov Regime-Switching model and the class of Archimedean
copulas have been widely applied to a variety of finance-related fields. The
Markov Regime-Switching model can reflect the reality that the underlying economy
is changing over time. Archimedean copulas are one of the most popular
classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies.
In the thesis, we first consider a discrete-time risk process based on the compound
binomial model with regime-switching. Some general recursive formulas
of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic
dominance relationship between random claims at different regimes, then we can
order ruin probabilities under different initial regimes.
Regarding capital allocation problems, which are important areas in finance
and risk management, this thesis studies the problems of optimal allocation of
policy limits and deductibles when the dependence structure among risks is modeled
by an Archimedean copula. By employing the concept of arrangement
increasing and stochastic dominance, useful qualitative results of the optimal
allocations are obtained.
Then we turn our attention to a new family of risk measures satisfying a set
of proposed axioms, which includes the class of distortion risk measures with
concave distortion functions. By minimizing the new risk measures, we consider
the optimal allocation of policy limits and deductibles problems based on the
assumption that for each risk there exists an indicator random variable which
determines whether the risk occurs or not. Several sufficient conditions to order
the optimal allocations are obtained using tools in stochastic dominance theory.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
30
Zhu, Jinxia. "Ruin theory under Markovian regime-switching risk models." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/b40203980.
Testo completo
31
Rong, Yian, and 戎軼安. "Applications of comonotonicity in risk-sharing and optimal allocation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/207205.
Testo completoAbstract (sommario):
Over the past decades, researchers in economics, financial mathematics and actuarial science have introduced results to the concept of comonotonicity in their respective fields of interest. Comonotonicity is a very strong dependence structure and is very often mistaken as a dependence structure that is too extreme and unrealistic. However, the concept of comonotonicity is actually a useful tool for solving several research and practical problems in capital allocation, risk sharing and optimal allocation.
The first topic of this thesis is focused on the application of comonotonicity in optimal capital allocation. The Enterprise Risk Management process of a financial institution usually contains a procedure to allocate the total risk capital of the company into its different business units. Dhaene et al. (2012) proposed a unifying capital allocation framework by considering some general deviation measures. This general framework is extended to a more general optimization problem of minimizing separable convex function with a linear constraint and box constraints. A new approach of solving this constrained minimization problem explicitly by the concept of comonotonicity is developed. Instead of the traditional Kuhn-Tucker theory, a method of expressing each convex function as the expected stop-loss of some suitable random variable is used to solve the optimization problem. Then, some results in convex analysis with infimum-convolution are derived using the result of this new approach.
Next, Borch's theorem is revisited from the perspective of comonotonicity. The optimal solution to the Pareto optimal risk-sharing problem can be obtained by the Lagrangian method or variational arguments. Here, I propose a new method, which is based on a Breeden-Litzanbeger type integral representation formula for increasing convex functions. It enables the transform of the objective function into a sum of mixtures of stop-losses. Necessary conditions for the existence of optimal solution are then discussed. The explicit solution obtained allows us to show that the risk-sharing problem is indeed a “point-wise” problem, and hence the value function can be obtained immediately using the notion of supremum-convolution in convex analysis.
In addition to the above classical risk-sharing and capital allocation problems, the problem of minimizing a separable convex objective subject to an ordering restriction is then studied. Best et al. (2000) proposed a pool adjacent violators algorithm to compute the optimal solution. Instead, we show that using the concept of comonotonicity and the technique of dynamic programming the solution can be derived in a recursive manner. By identifying the right-hand derivative of the convex functions with distribution functions of some suitable random variables, we rewrite the objective function into a sum of expected deviations. This transformation and the fact that the expected deviation is a convex function enable us to solve the minimizing problem.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Doctoral<br>Doctor of Philosophy
32
Basak, Rishi. "Environmental management systems and the intra-firm risk relationship." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0034/MQ64316.pdf.
Testo completo
33
Chen, Yiqing. "Study on insurance risk models with subexponential tails and dependence structures." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B42841768.
Testo completo
34
Wei, Zhenghong. "Empirical likelihood based evaluation for value at risk models." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/896.
Testo completo
35
Li, Tang, and 李唐. "Markov chain models for re-manufacturing systems and credit risk management." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203700.
Testo completo
36
Hao, Fangcheng, and 郝方程. "Options pricing and risk measures under regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4714726X.
Testo completo
37
Phipps, Shelley Ann. "An ethically flexible evaluation of unemployment insurance reform with constrained and unconstrained models of labour supply." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27509.
Testo completoAbstract (sommario):
The goal of this dissertation is to illustrate the importance and feasibility of conducting policy evaluations which pay attention to both efficiency and equity. Introducing an equity criterion necessarily involves introducing value judgements, but I suggest that objectivity can be maintained through the adoption of an 'ethically flexible' approach. That is, an analyst can avoid imposing his own particular values by explicitly conducting the evaluation from a number of different ethical positions.
This dissertation illustrates the feasibility of an ethically flexible approach by carrying out an evaluation of the proposals for the reform of the Canadian Unemployment Insurance (UI) programme made by the Macdonald and Forget Commissions. The evaluation proceeds in four stages:
1. Behavioural models which take account of the existence of unemployment and UI are developed.
2. The models are estimated using an appropriate Canadian data set.
3. The estimated models are used to simulate behavioural responses to UI reform.
4. Estimation and simulation results are used to carry out the ethically flexible welfare evaluation. Two household labour-supply models are used. The first assumes that observed unemployment is the outcome of utility-maximizing choices. The second introduces the possibility that demand-side constraints may interfere with supply-side choices. A form of switching regression with sample separation unknown is developed to allow estimation of 'constrained' labour-supply functions. Additional problems for estimation include a budget constraint which is non-linear as a result of the UI programme and a dependent variable, weeks of leisure (unemployment), which is limited to values between zero and fifty-two.
Both unconstrained and constrained models are estimated for single men, single women and couples, using linear expenditure systems and data from the 1982 Survey of Consumer Finance. Estimation results suggest that constrained labour-supply functions are less elastic than unconstrained functions, that there is no observable difference between the labour-supply behaviour of men and women in a constrained model, and that cross-effects are important in the determination of the labour-supply behaviour of couples. Estimated probabilities of constraint take an average value of (approximately) 80 percent.
The simulation of behavioural responses to UI reform using the estimated unconstrained labour-supply functions suggests that large reductions in unemployment might be anticipated. Simulation using the constrained labour-supply functions suggests that responses may be negligible.
Welfare evaluation measures are constructed for three ethical perspectives: The first is in the spirit of Utilitarianism; the second is in the spirit of John Rawls' theory of justice; the third is in the spirit of Robert Nozick's entitlement theory. The 'Utilitarian' measure is a mean of order r over the distribution of individual utilities. (Explicit interpersonal comparisons are required for these evaluations.) The 'Rawlsian' measure is a mean of order r over the distribution of individual incomes, censored at the poverty line to focus attention on the worst-off group. The 'Entitlement' measure is a measure of the distance between the distribution of individual costs (premiums) and benefits derived from UI.
Three factors are important in the- determination of the welfare-evaluation results. First, the ethical position adopted matters. Both UI reform proposals appear welfare-reducing from a Utilitarian perspective and welfare-improving from an Entitlement perspective. Second, for the Rawlsian and Utilitarian evaluations, the assumed degree of inequality aversion is important. Finally, assumptions made about the nature of unemployment are critical. This is most clearly illustrated by the Rawlsian results. If unemployment is assumed to be the outcome of utility-maximizing choices, then both reform proposals appear welfare-improving: poor people choose to work more and their incomes increase. If unemployment may be the result of demand-side constraints so that increases in employment are not possible, then UI reform merely results in reductions in income for the worst-off group.
These results illustrate the importance of both the equity and the efficiency dimensions of a policy evaluation. This thesis demonstrates the feasibility of conducting an objective policy evaluation which pays attention to both.<br>Arts, Faculty of<br>Vancouver School of Economics<br>Graduate
38
Powell, Robert. "Industry value at risk in Australia." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2007. https://ro.ecu.edu.au/theses/297.
Testo completoAbstract (sommario):
Value at Risk (VaR) models have gained increasing momentum in recent years. Market VaR is an important issue for banks since its adoption as a primary risk metric in the Basel Accords and the requirement that it is calculated on a daily basis. Credit risk modelling has become increasingly important to banks since the advent of Basel 11 which allows banks with sophisticated modelling techniques to use internal models for the purpose of calculating capital requirements. A high level of credit risk is often the key reason behind banks failing or experiencing severe difficulty. Conditional Value at Risk (CVaR) measures extreme risk, and is gaining popularity with the recognition that high losses are often impacted by a small number of extreme events.
39
Veraart, Luitgard Anna Maria. "Mathematical models for market making, option pricing and systemic risk." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613365.
Testo completo
40
Xu, Xiaochen, and 徐笑晨. "Estimation of structural parameters in credibility context using mixedeffects models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B4020361X.
Testo completo
41
Villaume, Erik. "Predicting customer level risk patterns in non-life insurance." Thesis, KTH, Matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-103590.
Testo completoAbstract (sommario):
Several models for predicting future customer profitability early into customer life-cycles in the property and casualty business are constructed and studied. The objective is to model risk at a customer level with input data available early into a private consumer’s lifespan. Two retained models, one using Generalized Linear Model another using a multilayer perceptron, a special form of Artificial Neural Network are evaluated using actual data. Numerical results show that differentiation on estimated future risk is most effective for customers with highest claim frequencies.
42
Parker, Bobby I. Mr. "Assessment of the Sustained Financial Impact of Risk Engineering Service on Insurance Claims Costs." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/100.
Testo completoAbstract (sommario):
This research paper creates a comprehensive statistical model, relating financial impact of risk engineering activity, and insurance claims costs. Specifically, the model shows important statistical relationships among six variables including: types of risk engineering activity, risk engineering dollar cost, duration of risk engineering service, and type of customer by industry classification, dollar premium amounts, and dollar claims costs.
We accomplish this by using a large data sample of approximately 15,000 customer-years of insurance coverage, and risk engineering activity. Data sample is from an international casualty/property insurance company and covers four years of operations, 2006-2009. The choice of statistical model is the linear mixed model, as presented in SAS 9.2 software. This method provides essential capabilities, including the flexibility to work with data having missing values, and the ability to reveal time-dependent statistical associations.
43
Li, Xiaofei 1972. "Three essays on the pricing of fixed income securities with credit risk." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=84523.
Testo completoAbstract (sommario):
This thesis studies the impacts of credit risk, or the risk of default, on the pricing of fixed income securities. It consists of three essays. The first essay extends the classical corporate debt pricing model in Merton (1974) to incorporate stochastic volatility (SV) in the underlying firm asset value and derive a closed-form solution for the price of corporate bond. Simulation results show that the SV specification for firm asset value greatly increases the resulting credit spread levels. Therefore, the SV model addresses one major deficiency of the Merton-type models: namely, at short maturities the Merton model is unable to generate credit spreads high enough to be compatible with those observed in the market. In the second essay, we develop a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. Our empirical results show that the model is successful at fitting actual corporate bond credit spreads. In addition, key properties of actual credit spreads are better captured by the model. Finally, the third essay proposes a model of interest rate swap spreads. The model accommodates both the default risk inherent in swap contracts and the liquidity difference between the swap and Treasury markets. The default risk and liquidity components of swap spreads are found to behave very differently: first, the default risk component is positively related to the riskless interest rate, whereas the liquidity component is negatively correlated with the riskless interest rate; second, although default risk accounts for the largest share of the levels of swap spreads, the liquidity component is much more volatile; and finally, while the default risk component has been historically positive, the liquidity component was negative for much of the 1990s and has become positive since the financial market turmoil in 1998.
44
Lo, Chi-ho, and 盧子豪. "Estimation of structural parameters for panel data in credibility context." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31557442.
Testo completo
45
McTaggart, Kevin Andrew. "Hydrodynamics and risk analysis of iceberg impacts with offshore structures." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/30733.
Testo completoAbstract (sommario):
The evaluation of design iceberg impact loads for offshore structures and the influence
of hydrodynamic effects on impact loads are examined. Important hydrodynamic effects include iceberg added mass, wave-induced oscillatory iceberg motions, and the influence of a large structure on the surrounding flow field and subsequent velocities of approaching icebergs. The significance of these phenomena has been investigated using a two-body numerical diffraction model and through a series of experiments modelling the drift of various sized icebergs driven by waves and currents approaching a large offshore structure. Relevant findings from the hydrodynamic studies have been incorporated into two probabilistic models which can be used to determine design iceberg collision events with a structure based on either iceberg kinetic energy upon impact or global sliding force acting on the structure. Load exceedence probabilities from the kinetic energy and sliding force models are evaluated using the second-order reliability method. Output from the probabilistic models can be used to determine design collision parameters and to assess whether more sophisticated modelling of various impact processes is required. The influence of the structure on velocities of approaching icebergs is shown to be significant
when the structure horizontal dimension is greater than twice the iceberg dimension. As expected, wave-induced oscillatory motions dominate the collision velocity for smaller icebergs but have a negligible effect on velocity for larger icebergs.<br>Applied Science, Faculty of<br>Civil Engineering, Department of<br>Graduate
46
Lin, Erlu. "Analysis of dividend payments for insurance risk models with correlated aggregate claims." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/b40203992.
Testo completo
47
Jiménez-Huerta, Diego. "Stochastic models and methods for the assessment of earthquake risk in insurance." Thesis, London School of Economics and Political Science (University of London), 2009. http://etheses.lse.ac.uk/302/.
Testo completoAbstract (sommario):
The problem of earthquake risk assessment and management in insurance is a challenging one at the interface of geophysics, engineering seismology, stochastics, insurance mathematics and economics. In this work, I propose stochastic models and methods for the assessment of earthquake risk from an insurer's point of view, where the aim is not to address problems in the financial mathematics and economics of risk selection, pricing, portfolio management, and risk transfer strategies such as reinsurance and securitisation, but to enable the latter through the characterisation of the foundation of any risk management consideration in insurance: the distribution of losses over a period of time for a portfolio of risks. Insurance losses are assumed to be generated by a loss process that is in turn governed by an earthquake process, a point process marked with the earthquake's hypocentre and magnitude, and a conditional loss distribution for an insurance portfolio, governing the loss size given the hypocentre and magnitude of the earthquake, and the physical characteristics of the portfolio as described in the individual policy records. From the modeling perspective, I examine the (non-trivial) minutiae around the infrastructure underpinning the loss process. A novel model of the earthquake process, a Poisson marked point process with spatial gamma intensity measure on the hypocentral space, and extensions of the Poisson and stress release models through the inclusion of hypocentral location in the mark, are proposed. I discuss the general architectural considerations for constructing the conditional loss distribution, and propose a new model as an alternative to the traditional ground motion attenuation and seismic vulnerability approach in engineering risk assessment. On the actuarial mathematics front, given a fully specified loss process, I address the problem of constructing simulation based and, where possible, analytical approximations to the distribution of portfolio losses over a period of time. I illustrate the applicability of the stochastic models and methods proposed in this work through the analysis of a residential homeowners property catastrophe portfolio exposed to earthquake risk in California. I construct approximations to the distribution of portfolio losses over a period of time under each of the three models of the earthquake process that I propose, and discuss their relative merits.
48
Terciyanli, Erman. "Alternative Mathematical Models For Revenue Management Problems." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610711/index.pdf.
Testo completoAbstract (sommario):
In this study, the seat inventory control problem is considered for airline networks from the
perspective of a risk-averse decision maker. In the revenue management literature, it is generally
assumed that the decision makers are risk-neutral. Therefore, the expected revenue is
maximized without taking the variability or any other risk factor into account. On the other
hand, risk-sensitive approach provides us with more information about the behavior of the
revenue. The risk measure we consider in this study is the probability that revenue is less
than a predetermined threshold level. In the risk-neutral cases, while the expected revenue
is maximized, the probability of revenue being less than such a predetermined level might
be high. We propose three mathematical models to incorporate the risk measure under consideration.
The optimal allocations obtained by these models are numerically evaluated in
simulation studies for example problems. Expected revenue, coefficient of variation, load factor
and probability of the poor performance are the performance measures in the simulation
studies. According to the results of these simulations, it shown that the proposed models can
decrease the variability of the revenue considerably. In other words, the probability of revenue
being less than the threshold level is decreased. Moreover, expected revenue can be increased
in some scenarios by using the proposed models. The approach considered in this thesis is especially proposed for small scale airlines because risk of obtaining revenue less than the
threshold level is more for this type of airlines as compared to large scale airlines.
49
Li, Yuming. "Univariate and multivariate measures of risk aversion and risk premiums with joint normal distribution and applications in portfolio selection models." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26110.
Testo completoAbstract (sommario):
This thesis gives the formal derivations of the so-called Rubinstein's measures of risk aversion and their multivariate generalizations. The applications of these measures in portfolio selection models are also presented.
Assuming that a decision maker's preferences can be represented by a unidimensional von Neumann and Morgenstern utility function, we consider a model with an uninsurable initial random wealth and an insurable risk. Under the assumption that the two random variables have a bivariate normal distribution, the second-order co-variance operator is developed from Stein/Rubinstein first-order covariance operator and is used to derive Rubinstein's measures of risk aversion from the approximations of risk premiums. Rubinstein's measures of risk aversion are proved to be the appropriate generalizations of the Arrow-Pratt measures of risk aversion.
In a portfolio selection model with two risky investments having a bivariate normal distribution, we show that Rubinstein's measures of risk aversion can yield the desirable characterizations of risk aversion and wealth effects on the optimal portfolio. These properties of Rubinstein's measures of risk aversion are analogous to those of the Arrow-Pratt measures of risk aversion in the portfolio selection model with one riskless and one risky investment.
In multi-dimensional decision problems, we assume that a decision maker's
preferences can be represented by a multivariate utility function. From the model with an uninsurable initial wealth vector and insurable risk vector having a joint normal distribution in the wealth space, we derived the matrix measures of risk aversion which are the multivariate extension of Rubinstein's measures of risk aversion. The derivations are based on the multivariate version of Stein/Rubinstein covariance operator developed by Gassmann and its second-order generalization to be developed in this thesis.
We finally present an application of the matrix measures of risk aversion in a portfolio selection model with a multivariate utility function and two risky investments.
In this model, if we assume that the random returns on the two investments and other random variables have a joint normal distribution, the optimal portfolio can be characterized by the matrix measures of risk aversion.<br>Business, Sauder School of<br>Graduate
50
Malwandla, Musa. "Loss distributions in consumer credit risk : macroeconomic models for expected and unexpected loss." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20414.
Testo completoAbstract (sommario):
This thesis focuses on modelling the distributions of loss in consumer credit arrangements, both at an individual level and at a portfolio level, and how these might be influenced by loan-specific factors and economic factors. The thesis primarily aims to examine how these factors can be incorporated into a credit risk model through logistic regression models and threshold regression models. Considering the fact that the specification of a credit risk model is influenced by its purpose, the thesis considers the IFRS 7 and IFRS 9 accounting requirements for impairment disclosure as well as Basel II regulatory prescriptions for capital requirements. The thesis presents a critique of the unexpected loss calculation under Basel II by considering the different ways in which loans can correlate within a portfolio. Two distributions of portfolio losses are derived. The Vašíček distribution, which is the assumed in Basel II requirements, was originally derived for corporate loans and was never adapted for application in consumer credit. This makes it difficult to interpret and validate the correlation parameters prescribed under Basel II. The thesis re-derives the Vašíček distribution under a threshold regression model that is specific to consumer credit risk, thus providing a way to estimate the model parameters from observed experience. The thesis also discusses how, if the probability of default is modelled through logistic regression, the portfolio loss distribution can be modelled as a log-log-normal distribution.