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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.
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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.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.
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Arvidsson, Hanna, and Sofie Francke. "Dependence in non-life insurance." Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120621.
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Hagsjö, Renberg Oscar, and Oscar Hermansson. "Large claims in non-life insurance." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-215492.
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It is of outmost importance for an insurance company to apply a fair pricing policy. If the price is too high, valuable customers are lost to other insurance companies while if it’s too low – it nets a negative profit. To achieve a good pricing policy, information regarding claim size history for a given type of customer is required. A problem arises as large extremal events occur and affects the claim size data. These extremal events take shape in individually large claim sizes that by themselves can alter the distribution for what certain groups of individuals are expected to cost. A remedy for this is to apply what is called a large claim limit. Any claim exceeding this limit is thought of as being outside the scope of what is captured by the original distribution of the claim size. These exceeding claims are treated separately and have their cost distributed across all insurance takers, rather than just the group they belong to. So, where exactly do you draw this limit? Do you treat the entire claim size this way (exclusion) or just the bit that is exceeding the threshold (truncation)? These questions are treated and answered in this master’s thesis for Trygg-Hansa. For each product code, a limit was achieved in addition to which method for exceeding data that was best to use.Det är oerhört viktigt för ett försäkringsbolag att kunna tillämpa en god prissättning. Är priset för högt så förloras kunder till andra försäkringsbolag, och är den underprisad är det en förlustaffär. För att kunna sätta bra priser krävs information om vilka samt hur stora skador som kan tänkas inträffa för en given kundprofil. Ett problem uppstår när stora extremfall påverkar skadedatan. Dessa extremfall yttrar sig genom enskilda storskador som kan komma att påverka prissättningen för en hel grupp då distributionen för vad gruppen förväntas kosta kan ändras. Detta problem kan lösas genom att införa en storskadegräns till skadedatan. Skador över denna gräns räknas som extremfall och utanför ramen av vad den ursprungliga distributionen för skadorna beskriver. De hanteras separat och låter sin kostnad fördelas över samtliga försäkringstagare. Men vart dras denna gräns? Ska man behandla hela den överstigande kostnaden på detta sätt (exkludering) eller bara den biten av skadan som går över storskadegränsen (trunkering)? Dessa frågor behandlas och besvaras i denna masteruppsats i uppdrag åt Trygg-Hansa. För de olika produkttypkoderna beräknades varsin storskadegräns samt metod för överskridande data.
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Osman, Abdelghafour Mohamed. "Structured products: Pricing, hedging and applications for life insurance companies." Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119969.
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Pansera, Jérôme. "Local risk minimization, consistent interest-rate modeling, and applications to life insurance." Diss., University of Iowa, 2008. https://ir.uiowa.edu/etd/15.
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This thesis studies local risk minimization, consistent interest-rate modeling, and their applications to life insurance.
Part I considers local risk minimization, which is one possible approach to price and hedge claims in incomplete markets. In this first part, our two main results are Propositions 3.6 and 4.3: they provide an easy way to compute locally risk-minimizing hedging strategies for common life-insurance products in discrete time and in continuous time, respectively.
Part II considers consistent interest-rate modeling; that is, interest-rate models in which a change in the yield curve can be explained by a change in the state variable, without changing the parameters of the model. In this second part, we present a single-factor interest-rate model (jointly specified under the physical and the risk-neutral probability measures), which allows for observation errors. Our main result is an algorithm to estimate the hidden values of the state variable, as well as the five parameters of our model. We also outline how our results can be extended to the multi-factor case.
Part III combines the results of Parts I and II in a numerical example. In this example, we compute a locally risk-minimizing hedging strategy for a life annuity under stochastic interest rates. We assume that the insurance company is trying to hedge this product by trading zero-coupon bonds of various maturities. Since a perfect hedge is impossible in this case, we obtain (by simulation) the distribution of the cost resulting from the ``mis-hedge''. This distribution is with respect to the physical probability measure, while most of the existing literature considers it under a risk-neutral measure.
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Gip, Orreborn Jakob. "Asset-Liability Management with in Life Insurance." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-215339.
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In recent years, new regulations and stronger competition have further increased the importance of stochastic asset-liability management (ALM) models for life insurance firms. However, the often complex nature of life insurance contracts makes modeling to a challenging task, and insurance firms often struggle with models quickly becoming too complicated and inefficient. There is therefore an interest in investigating if, in fact, certain traits of financial ratios could be exposed through a more efficient model. In this thesis, a discrete time stochastic model framework, for the simulation of simplified balance sheets of life insurance products, is proposed. The model is based on a two-factor stochastic capital market model, supports the most important product characteristics, and incorporates a reserve-dependent bonus declaration. Furthermore, a first approach to endogenously model customer transitions is proposed, where realized policy returns are used for assigning transition probabilities. The model's sensitivity to different input parameters, and ability to capture the most important behaviour patterns, are demonstrated by the use of scenario and sensitivity analyses. Furthermore, based on the findings from these analyses, suggestions for improvements and further research are also presented.Införandet av nya regelverk och ökad konkurrens har medfört att stokastiska ALM-modeller blivit allt viktigare för livförsäkringsbolag. Den ofta komplexa strukturen hos försäkringsprodukter försvårar dock modelleringen, vilket gör att många modeller anses vara för komplicerade samt ineffektiva, av försäkringsbolagen. Det finns därför ett intresse i att utreda om egenskaper hos viktiga finansiella nyckeltal kan studeras utifrån en mer effektiv och mindre komplicerad modell. I detta arbete föreslås ett ramverk för stokastisk modellering av en förenklad version av balansräkningen hos typiska livförsäkringsbolag. Modellen baseras på en stokastisk kapitalmarknadsmodell, med vilken såväl aktiepriser som räntenivåer simuleras. Vidare så stödjer modellen simulering av de mest väsentliga produktegenskaperna, samt modellerar kundåterbäring som en funktion av den kollektiva konsolideringsgraden. Modellens förmåga att fånga de viktigaste egenskaperna hos balansräkningens ingående komponenter undersöks med hjälp av scenario- och känslighetsanalyser. Ytterligare undersöks även huruvida modellen är känslig för förändringar i olika indata, där fokus främst tillägnas de parametrar som kräver mer avancerade skattningsmetoder.
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Barnholdt, Jacob, and Josefin Grafford. "Predicting Large Claims within Non-Life Insurance." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-228983.
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This bachelor thesis within the field of mathematical statistics aims to study the possibility of predicting specifically large claims from non-life insurance policies with commercial policyholders. This is done through regression analysis, where we seek to develop and evaluate a generalized linear model, GLM. The project is carried out in collaboration with the insurance company If P&C Insurance and most of the research is conducted at their headquarters in Stockholm. The explanatory variables of interest are characteristics associated with the policyholders. Due to the scarcity of large claims in the data set, the prediction is done in two steps. Firstly, logistic regression is used to model the probability of a large claim occurring. Secondly, the magnitude of the large claims is modelled using a generalized linear model with a gamma distribution. Two full models with all characteristics included are constructed and then reduced with computer intensive algorithms. This results in two reduced models, one with two characteristics excluded and one with one characteristic excluded.Det här kandidatexamensarbetet inom matematisk statistik avser att studera möjligheten att predicera särskilt stora skador från sakförsäkringspolicys med företag som försäkringstagare. Detta görs med regressionsanalys, där vi ämnar att utveckla och bedöma en generaliserad linjär modell, GLM. Projektet utförs i samarbete med försäkringsbolaget If Skadeförsäkring och merparten av undersökningen sker på deras huvudkontor i Stockholm. Förklaringsvariablerna som är av intresse att undersöka är egenskaper associerade med försäkringstagarna. På grund av sällsynthet av storskador i datamängden görs prediktionen i två steg. Först används logistisk regression för att modellera sannolikheten för en storskada att inträffa. Sedan modelleras storskadornas omfattning genom en generaliserad linjär modell med en gammafördelning. Två grundmodeller med alla förklaringsvariabler konstrueras för att sedan reduceras med datorintensiva algoritmer. Det resulterar i två reducerade modeller, med två respektive en kundegenskap utesluten.
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Rinkevičiūtė, Laima. "Ne gyvybės draudimo analizė Lietuvoje." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060606_150230-24295.
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Insurance market in Lithuania is evolving yet, but this process is quite rapid.
The destination of this work – analysis of non life insurance in Lithuania, which we will dispense, when we will interpret statistical information of insurance, also we will analyze paying capacity of non life insurance companies. Insurance companies calculate future’s contribution using data of past period. It would be better to correct contribution according to predictive future’s number of contracts and loss. So the number of contracts and loss, signed by Lithuanian insurance companies each quarter, are studied as time series. Several time series models were created for three principal kinds of insurance (Motor Third Party Liability Insurance, Land vehicles other than railway rolling stock Insurance, Property Insurance) and the one that meets the reality best was selected.
We will analyze variation of number of non life insurance companies, number of paid losses, number of signed contributions and number of contracts. After analyses of Insurance market’s indicators, we get strong tendency that Insurance market becomes more stable.
After analysis of insurance companies’ paying capacity we got, that two close private companies - “Baltic Polis” and “Industrijos garantas” – was close to bankrupt in 2004 year.
After forecasting number of Motor Third Party Liability Insurance’s and Land vehicles other than railway rolling stock Insurance’s contracts we got that Autoregressive model is the best for... [to full text]
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Hardin, Patrik, and Sam Tabari. "Modelling Non-life Insurance Policyholder Price Sensitivity : A Statistical Analysis Performed with Logistic Regression." Thesis, KTH, Matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-209773.
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This bachelor thesis within mathematical statistics studies the possibility of modelling the renewal probability for commercial non-life insurance policyholders. The project was carried out in collaboration with the non-life insurance company If P&C Insurance Ltd. at their headquarters in Stockholm, Sweden. The paper includes an introduction to underlying concepts within insurance and mathematics and a detailed review of the analytical process followed by a discussion and conclusions. The first stages of the project were the initial collection and processing of explanatory insurance data and the development of a logistic regression model for policy renewal. An initial model was built and modern methods of mathematics and statistics were applied in order obtain a final model consisting of 9 significant characteristics. The regression model had a predictive power of 61%. This suggests that it to a certain degree is possible to predict the renewal probability of non-life insurance policyholders based on their characteristics. The results from the final model were ultimately translated into a measure of price sensitivity which can be implemented in both pricing models and CRM systems. We believe that price sensitivity analysis, if done correctly, is a natural step in improving the current pricing models in the insurance industry and this project provides a foundation for further research in this area.Detta kandidatexamensarbete inom matematisk statistik undersöker möjligheten att modellera förnyelsegraden för kommersiella skadeförsärkringskunder. Arbetet utfördes i samarbete med If Skadeförsäkring vid huvudkontoret i Stockholm, Sverige. Uppsatsen innehåller en introduktion till underliggande koncept inom försäkring och matematik samt en utförlig översikt över projektets analytiska process, följt av en diskussion och slutsatser. De huvudsakliga delarna av projektet var insamling och bearbetning av förklarande försäkringsdata samt utvecklandet och tolkningen av en logistisk regressionsmodell för förnyelsegrad. En första modell byggdes och moderna metoder inom matematik och statistik utfördes för att erhålla en slutgiltig regressionsmodell uppbyggd av 9 signifikanta kundkaraktäristika. Regressionsmodellen hade en förklaringsgrad av 61% vilket pekar på att det till en viss grad är möjligt att förklara förnyelsegraden hos försäkringskunder utifrån dessa karaktäristika. Resultaten från den slutgiltiga modellen översattes slutligen till ett priskänslighetsmått vilket möjliggjorde implementering i prissättningsmodeller samt CRM-system. Vi anser att priskänslighetsanalys, om korrekt genomfört, är ett naturligt steg i utvecklingen av dagens prissättningsmodeller inom försäkringsbranschen och detta projekt lägger en grund för fortsatta studier inom detta område.
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Gyllenberg, Felix, and Åström Leonard Rudolf. "INTEREST RATE RISK : A comparative study aimed at finding the most crucial shift in interest rate curves for a life insurance company." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-160248.
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Risk management is applied in many financial institutions under regulatory supervision. Life insurance companies face many challenges to ensure policy holders of future payouts. The inverted balance sheet of life insurance companies imply that the policy holder pay premiums in advance to the insurance company to later receive payouts at the age of retirement. This means a great responsibility for the life insurance company to be able to meet future liabilities. Due to this, one of the largest risks facing a life insurance company is the interest rate risk. Future liabilities depend on the interest rates and the difference in duration in assets and liabilities creates an imperfect negative correlation between the movements in assets and liabilities when the interest rate change. The bond market holds different types of bonds such as government bonds, housing bonds and corporate bonds with different maturities within each subgroup. The relationship between these subgroups and maturities within these subgroups are interesting to investigate in a forecasting point of view. This relationship is usually referred to as the term structure of interest rates and changes in the term structure are referred to as shifts. This thesis aims to find which of the three shifts, level, slope and curvature, that is most important to capture in interest rate models. This is investigated using three different simulation techniques and the results show that the first shift representing a level shift of the whole term structure has the largest effect on Skandia’s balance sheet.
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Guimarães, Sérgio Rangel. "Fundamentação técnica e atuarial dos seguros de vida : um estudo comparativo entre o seguro de vida individual e o seguro de vida em grupo no Brasil." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2003. http://hdl.handle.net/10183/3227.
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A indústria de seguros é uma atividade econômica relativamente jovem, possuindo raízes na revolução industrial. O desenvolvimento dessa indústria ocorreu de forma bastante intensa durante o século passado, quando a atividade passou a ser inserida na área de gestão de riscos. As Companhias de Seguros que trabalham nesse ambiente de negócio fundamentam todo o processo de precificação dos seus produtos em rígidas bases técnicas e atuariais. O presente trabalho dedica-se ao estudo dessas questões, abordando especificamente os seguros de vida, com ênfase à cobertura de morte. A pesquisa tem por objetivo comparar duas modalidades distintas de seguros que são ofertadas ao mercado: o seguro de vida individual e o seguro de vida em grupo. Embora ofereçam aos consumidores coberturas bastante similares, ambas as modalidades devem obedecer a requisitos e princípios técnicos diferenciados por parte das instituições que fazem a sua gestão.The insurance industry is a relatively young economic activity; its bases are found in the industrial revolution. The development of such industry occurred in a very intense way in the last century, when the activity started being placed in the area of management of risks. The insurance companies that work in this business environment base the whole pricing process of their products on rigid technical and actuarial bases. The present work aims at studying these questions, focusing on the life insurance, with emphasis on the death coverage. The research intends to explore and compare two distinct modalities of insurance that are offered to the market: the individual life insurance and the group life insurance. Even though they offer similar coverage, they must fulfill requirements and different technical principles ruled by the institutions which are responsible for their management.
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Adams, Joseph Allen. "A Matched Payout Model for Investment, Consumption, and Insurance with a Risky Annuity Income." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7474.
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We introduce a new insurance instrument allowing retirees to hedge against risk of mortality and risk of default. At retirement, the retiree is allowed to purchase an annuity that provides a defaultable income stream over his lifetime. The time of mortality and time of default are both uncertain, but are accompanied by determined hazard rates. The retiree will make consumption and investment choices throughout his lifetime, which have certain restrictions: the retiree can never enter a bankruptcy state (negative total wealth), and the investment choices are made in a risk-free financial instrument (such as a treasury bill or bond) and a risky instrument (such as commodities or stock). The retiree also makes insurance premium payments which hedge against mortality and default risks simultaneously. This new form of insurance is one which can be implemented by financial institutions as a means for retirees to protect their illiquid assets. In doing so, we calculate the optimal annuity rate a retiree should purchase to maximize his utility of consumption and bequest.Throughout the paper, we develop stochastic control models for a retiree's optimal investment and consumption policies over an uncertain planning horizon in several models which may or may not allow for insurance purchases. We find exact solutions to several models, and apply dynamic programming and the logarithmic transformation to other models to find numerical solutions when constraints are needed. We also analyze the effects of loading on insurance, analyzing the effects of more expensive insurance on the retiree's control policies and value functions. In particular, we will consider the model in which the retiree can purchase life insurance and credit default insurance (in the form of a credit default swap, or CDS) separately to hedge against life events. CDS's do not exist for annuities, but we extend this model by incorporating life insurance and the CDS into a single entity, which can be a viable, and realistic, option to hedge against risk. This model is beneficial in providing a solution to the annuity problem by showing that minimal annuity purchase is optimal.
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Widing, Björn, and Jimmy Jansson. "Valuation Practices of IFRS 17." Thesis, KTH, Matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-224211.
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This research assesses the IFRS 17 Insurance Contracts standard from a mathematical and actuarial point of view. Specifically, a valuation model that complies with the standard is developed in order to investigate implications of the standard on financial statements of insurance companies. This includes a deep insight into the standard, construction a valuation model of a fictive traditional life insurance product and an investigation of the outcomes of the model. The findings show firstly that an investment strategy favorable for valuing insurance contracts according to the standard may conflict with the Asset & Liability Management of the firm. Secondly, that a low risk adjustment increases the contractual service margin (CSM) and hence the possibility of smoothing profits over time. Thirdly, that the policy for releasing the CSM should take both risk-neutral and real assumptions into account.I denna rapport ansätts redovisningsstandarden IFRS 17 Insurance Contracts utifrån ett matematiskt och aktuariellt perspektiv. En värderingsmodell som överensstämmer med standarden konstrueras för att undersöka standardens implikationer på ett försäkringsbolags resultaträkning. Detta inkluderar en fördjupning i standarden, konstruktion och modellering av en fiktiv traditionell livförsäkringsprodukt samt undersökning av resultaten från modellen. Resultaten visar att det finns en möjlig konflikt mellan investeringsstrategier som är gynnsamma med avseende på värdering enligt standarden och ett försäkringsbolags tillgångs- och skuldförvaltning. Vidare leder en låg riskjustering till en högre avtalsmässig servicemarginal (CSM) vilket ökar möjligheten att utjämna vinster över tid. Slutligen bör policyn för hur CSM frisläpps beakta både risk-neutrala och verkliga antaganden.
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Schreiber, Irene. "Risk-minimization for life insurance liabilities." Diss., lmu, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-153192.
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Melo, Rafael Sobral. "Aplicação da lei de mortalidade de PERKS à experiência brasileira no ramo vida." Master's thesis, Instituto Superior de Economia e Gestão, 2009. http://hdl.handle.net/10400.5/1701.
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Mestrado em Ciências ActuariaisO objectivo deste trabalho é trazer alguns conceitos e elementos utilizados na Matemática Actuarial sob uma óptica contínua, discorrendo pela análise populacional, pelos arranjos securitários - anuidades e seguros - e culminando em um plano de aposentadoria. Para isso, utilizou-se da Lei de Mortalidade de Perks em modelos embasados no mercado brasileiro de fundos de pensão e seguradoras.
The objective of this work is to bring some concepts and elements used in the Actuarial Mathematics on the continuous focus, beginning in population analysis, the security nets -annuities and life insurance - and culminating in a retirement plan. For that, we used the Mortality Law of Perks in models based in the Brazilian market of pension funds and insurance companies.
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Björkwall, Susanna. "Stochastic claims reserving in non-life insurance : Bootstrap and smoothing models." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-55347.
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In practice there is a long tradition of actuaries calculating reserve estimates according to deterministic methods without explicit reference to a stochastic model. For instance, the chain-ladder was originally a deterministic reserving method. Moreover, the actuaries often make ad hoc adjustments of the methods, for example, smoothing of the chain-ladder development factors, in order to fit the data set under analysis. However, stochastic models are needed in order to assess the variability of the claims reserve. The standard statistical approach would be to first specify a model, then find an estimate of the outstanding claims under that model, typically by maximum likelihood, and finally the model could be used to find the precision of the estimate. As a compromise between this approach and the actuary's way of working without reference to a model the object of the research area has often been to first construct a model and a method that produces the actuary's estimate and then use this model in order to assess the uncertainty of the estimate. A drawback of this approach is that the suggested models have been constructed to give a measure of the precision of the reserve estimate without the possibility of changing the estimate itself. The starting point of this thesis is the inconsistency between the deterministic approaches used in practice and the stochastic ones suggested in the literature. On one hand, the purpose of Paper I is to develop a bootstrap technique which easily enables the actuary to use other development factor methods than the pure chain-ladder relying on as few model assumptions as possible. This bootstrap technique is then extended and applied to the separation method in Paper II. On the other hand, the purpose of Paper III is to create a stochastic framework which imitates the ad hoc deterministic smoothing of chain-ladder development factors which is frequently used in practice.
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Straß, Belinda. "Comparison of prices of life insurances using different mortality rates models." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-39911.
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Capturing mortality became a crucial modelling problem throughout the years due to the raising demand of life insurances and annuities. Fitting three models, namely, logistic, Heligman– Pollard HP4 and power–exponential model, to real life data shows that latter two models represent the actual data quite well. Pricing a term life insurance and a whole life annuity, implemented using the MATLAB software, based on these models ends in the result that the Heligmann–Pollard HP4 model is the less preferable model, in perspective of an insured, than the logistic or power–exponential ones.
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Tillier, Charles. "Processus et indicateurs de risque en assurance non-vie et sécurité alimentaire." Thesis, Paris 10, 2017. http://www.theses.fr/2017PA100192.
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L'analyse des risques est devenu un enjeu majeur dans notre société. Quels que soient les champs d'application dans lesquels une situation à risque peut survenir, les mathématiques et plus particulièrement les statistiques et les probabilités se révèlent être des outils essentiels. L'objet principal de cette thèse est de développer des indicateurs de risque pertinents et d'étudier les propriétés extrémales de processus intervenant dans deux domaines d'applications : en risque alimentaire et en assurance. La théorie du risque se situe entre l'analyse des valeurs extrêmes et la théorie des variables aléatoires à variations régulières ou à queues lourdes. Dans le premier chapitre, on définit les éléments clefs de la théorie du risque ainsi que la notion de variation régulière et on introduit différents modèles liés au risque alimentaire qui seront étudiés dans les chapitres 2 et 3. Le chapitre 2 présente les travaux effectués avec Olivier Wintenberger. Pour des classes de processus stochastiques, sous des hypothèses de variations régulières, on développe une méthode qui permet d'obtenir des équivalents asymptotiques en horizon fini d'indicateurs de risque en assurance et en risque alimentaire tels que la probabilité de ruine, le "temps passé au dessus d'un seuil" ou encore la "sévérité de la ruine". Le chapitre 3 se concentre sur des modèles en risque alimentaire. Précisément, on étudie les propriétés extrémales de différentes généralisations d'un processus d'exposition à un contaminant nommé KDEM pour Kinetic Dietary Exposure Model proposé par Patrice Bertail et ses co-auteurs en 2008. Sous des hypothèses de variations régulières, on propose des équivalents asymptotiques du comportement de queue et de l'indice extrémal du processus d'exposition. Enfin, le chapitre 4 passe en revue différentes techniques statistiques particulièrement adaptées à l'étude du comportement extrémal de certains processus de Markov. Grâce à des propriétés de régénérations, il est possible de découper le chemin des observations en blocs indépendants et identiquement distribués et de n'étudier ainsi que le processus sur un bloc. Ces techniques s'appliquent même si la chaîne de Markov n'est pas atomique. On se concentre ici sur l'estimation de l'indice de queue et de l'indice extrémal. On illustre la performance de ces techniques en les appliquant sur deux modèles - en assurance et en finance - dont on connaît les résultats théoriquesRisk analyses play a leading role within fields such as dietary risk, hydrology, nuclear security, finance and insurance and is more and more present in theapplications of various probability tools and statistical methods. We see a significant impact on the scientific literature and on public institutions in the past years. Risk theory, which is really close to extreme value analysis, typically deals with the occurrences of rare events which are functions of heavy-tailed random variables, for example, sums or products of regularly varying random variables. The purpose of this thesis is the following : to develop revelant risk indicators and to study the extremal properties of stochastic processes used in dietary risk assessment and in insurance. In Chapter 1, we present the main tools used in risk theory and the notion of regular variation and introduce different models involved in dietary risk assessment, which will be specifically studied in Chapters 2 and 3. Chapter 2 presents a joint work with Olivier Wintenberger. For a particular class of stochastic processes, under the assumption of regular variation, we propose a method that gives way to asymptotic equivalents on a finite-time horizon of risk indicators such as the ruin probability, the Expected Time over a Threshold or the Expected Severity of the ruin. Chapter 3 focuses on dietary risk models. To be precise, we study the extremal properties of an extension of a model called KDEM for Kinetic Dietary Exposure Model introduced by Patrice Bertail and his co-authors in 2008. Under the assumption of regular variation, we provide asymptotic equivalents for the tail behavior and the extremal index of the exposure process. In Chapter 4, we review different statistical tools specifically tailored for the study of the extremal behavior of Markov processes. Thanks to regeneration properties, we can split the path of observations into blocks which are independent and identically distributed. This technic still works even if the Markov chain is not atomic. We focus here on the estimation of the tail index and the extremal index. We illustrate the performance of these technics applying them on two models in insurance and finance for which we know the theoritical results
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Jori, Mar. "Life Settlements y Viaticals." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/132000.
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Esta tesis doctoral se enmarca en un novedoso mercado basado en la compra/venta de pólizas de vida donde se comercializan dos tipos de productos: el Viatical y el Settlement.
Un primer análisis se centra en el desarrollo de unos modelos económicos de optimización basados en la maximización de la utilidad esperada de un tomador para determinar si resulta óptimo o no vender su póliza de vida en el mercado secundario. La venta de la póliza viene determinada por múltiples factores personales y de mercado del tomador del seguro de vida.
Un segundo análisis se centra en la definición de los riesgos a los que incurre el inversor al invertir tanto en Viaticals como en Life Settlements. Se destaca el riesgo de longevidad, muy elevado en este tipo de operaciones. Se propone, por tanto, la medición de dicho riesgo mediante un instrumento denominado modified life extension duration.This thesis focuses on a new market where the policyholder can sell his life insurance policy by hiring two kinds of contracts: a Viatical if the insured is a terminally ill person or a Life Settlement if he is impaired. A first study concerns the optimal decision rules for a policyholder who wants to sell his life insurance policy. We present two economic models, the first model is focused on Viaticals and is treated in discrete setting, the second model is focused on Life Settlements and should be treated in continuous time. In both models a terminally ill/impaired policyholder has to decide whether or not to sell his life insurance policy in the secondary market and in case of selling it when it is optimally better to do it. A second study concerns the risks assumed by the investor in Viaticals or Life Settlements. The main risk is the longevity risk. We propose a measure to value this risk called modified life extension duration. This measure determines the loss in the Life Settlement/Viatical value because of an increase of the life expectancy of the insured.
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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.
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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.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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Guambe, Calisto. "Optimal investment, consumption and life insurance in a Lévy market." Diss., 2015. http://hdl.handle.net/2263/50312.
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The purpose of this dissertation is to solve an optimal investment, consumption and life insurance problem described by jump-diffusion processes in two settings.
First, we consider a problem with random parameters of a wage earner who wants to save to his beneficiary for his death. Using one risk-free asset and one risky asset price given by a geometric jump-diffusion process, we obtain the optimal strategy via the dynamic programming approach, combining the Hamilton-Jacobi-Bellman equation with a backward stochastic differential equation with jumps.
Secondly, we discuss the optimal investment, consumption and life insurance problem with capital constraints. The problem consists of one risk-free asset and two risky asset prices defined in an independent Brownian motion and Poisson process. We derive the optimal strategy of the unconstrained problem via martingale approach, from which, the problem with capital constraint is solved applying the option based portfolio insurance method.Dissertation (MSc)--University of Pretoria, 2016.
Mathematics and Applied Mathematics
MSc
Unrestricted
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Gatzert, Nadine Verena. "Implicit options in life insurance : valuation and risk assessment /." 2007. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=016095567&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Fischer, Tom [Verfasser]. "Valuation and risk management in life insurance / von Tom Fischer." 2004. http://d-nb.info/970361610/34.
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"An efficient valuation of participating life insurance contracts under Lévy process." 2010. http://library.cuhk.edu.hk/record=b5896646.
Full textAbstract:
Wong, Shiu Fung."July 2010."
Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.
Includes bibliographical references (leaves 36-38).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Participating policy --- p.4
Chapter 3 --- Levy Process and its use in financial modelling --- p.8
Chapter 3.1 --- Levy process in asset modelling --- p.8
Chapter 3.2 --- Levy process in derivative pricing --- p.11
Chapter 3.2.1 --- Review of FFT methods in option pricing --- p.12
Chapter 3.2.2 --- Expectation using FFT --- p.13
Chapter 4 --- Network methodology --- p.17
Chapter 4.1 --- Asset dynamic: Network Approach --- p.17
Chapter 4.1.1 --- Transition probability by FFT --- p.18
Chapter 4.1.2 --- Example in American option pricing --- p.19
Chapter 4.2 --- Extended Network for Participating Contract --- p.20
Chapter 4.3 --- Practical network construction --- p.22
Chapter 4.3.1 --- Modified network-drift offsetting --- p.23
Chapter 4.3.2 --- Logarithmic scale network --- p.25
Chapter 4.4 --- Incorporating surrender rights and mortality --- p.26
Chapter 4.4.1 --- Surrender right --- p.26
Chapter 4.4.2 --- Mortality --- p.27
Chapter 4.5 --- Proof of convergence --- p.28
Chapter 5 --- Numerical Results --- p.32
Chapter 5.1 --- The Black and Scholes model --- p.33
Chapter 5.2 --- The Merton's Jump diffusion model --- p.33
Chapter 5.3 --- Variance gamma model --- p.34
Chapter 6 --- Conclusion --- p.35
Bibliography --- p.36
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Zhang, Aihua [Verfasser]. "Stochastic optimization in finance and life insurance : applications of the Martingale method / Aihua Zhang (Chang)." 2008. http://d-nb.info/989269663/34.
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Gschlößl, Susanne [Verfasser]. "Hierarchical Bayesian spatial regression models with applications to non-life insurance / Susanne Gschlößl." 2006. http://d-nb.info/978924576/34.
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Christiansen, Marcus C. [Verfasser]. "A joint analysis of financial and biometrical risks in life insurance / vorgelegt von Marcus Christian Christiansen." 2007. http://d-nb.info/988046946/34.
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"Three essays on insurance asset liability management." Thesis, 2008. http://library.cuhk.edu.hk/record=b6074654.
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The key objective of insurance company on money management is asset liability management, as policy asset is solely for paying policy liability. It is true whether it is in case of life insurance, general insurance, or reinsurance. The difficulty of achieving such objective is that the exact cash flow and the exact duration of policy liability are unknown ex ante that requires the asset manager's a good quantitative, financial skill. What is worse is that the variations of cash flow and duration can be huge that is demanding on the asset manager's quantitative, financial skill. Quantitative problem is difficult but qualitative problem can be even more difficult. The specialist problem in insurance industry, which is also known as agency problem in information economics, is notorious. It is because a specialist may no longer work for the insurance company when the long term liability is due and the existing liability portfolio is always composed of myriad policies liability.The purpose of this thesis is to try to provide solutions to three critical problems in insurance industry. (1) China is the most booming country for insurance at the moment. So, it is selected for discussing about the most difficult problem in modern finance---specialist problem. A structural approach is devised in this thesis to solve such problem. The solution can be generalized to all countries. (2) As many people argue about that modern finance is inapplicable to emerging market, such as China, especially when there are capital account and currency controls, the bond market of China is selected to provide evidence that modern finance is applicable to emerging market even both the capital account and the currency of the country are controlled by the government. (3) The last part of this thesis provides a breakthrough solution to price insurer default option, an embedded option, in insurance company using observable credit default swap price, as the traditional approach needs statistical assumption that is subjective.
Li, Wing Ping Desmond.
Adviser: Frank Youhua Chen.
Source: Dissertation Abstracts International, Volume: 70-06, Section: A, page: 2169.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references (leaves 64-65).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.
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Helwich, Marko [Verfasser]. "Durational effects and non-smooth semi-Markov models in life insurance / vorgelegt von Marko Helwich." 2007. http://d-nb.info/989745813/34.
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