Academic literature on the topic 'Chain-ladder'

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Journal articles on the topic "Chain-ladder"

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Taylor, Greg. "Chain Ladder Bias." ASTIN Bulletin 33, no. 02 (2003): 313–30. http://dx.doi.org/10.2143/ast.33.2.503695.

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The chain ladder forecast of outstanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 5 shows that, under rather general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.
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Taylor, Greg. "Chain Ladder Bias." ASTIN Bulletin 33, no. 2 (2003): 313–30. http://dx.doi.org/10.1017/s0515036100013489.

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The chain ladder forecast of outstanding losses is known to be unbiased under suitable assumptions. According to these assumptions, claim payments in any cell of a payment triangle are dependent on those from preceding development years of the same accident year. If all cells are assumed stochastically independent, the forecast is no longer unbiased. Section 5 shows that, under rather general assumptions, it is biased upward. This result is linked to earlier work on some stochastic versions of the chain ladder.
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Quarg, Gerhard, and Thomas Mack. "Munich chain ladder." Blätter der DGVFM 26, no. 4 (2004): 597–630. http://dx.doi.org/10.1007/bf02808969.

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Taylor, Greg. "BAYESIAN CHAIN LADDER MODELS." ASTIN Bulletin 45, no. 1 (2014): 75–99. http://dx.doi.org/10.1017/asb.2014.25.

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AbstractThe literature on Bayesian chain ladder models is surveyed. Both Mack and cross-classified forms of the chain ladder are considered. Both cases are examined in the context of error terms distributed according to a member of the exponential dispersion family. Tweedie and over-dispersed Poisson errors follow as special cases. Bayesian cross-classified chain ladder models may randomise row, column or diagonal parameters. Column and diagonal randomisation has been largely absent from the literature until recently. The present paper allows randomisation of row and column parameters. The Bayes estimator, the linear Bayes (credibility) estimator, and the MAP estimator are shown to be identical in the Mack case, and in the cross-classified case provided that the error terms are Tweedie distributed. In the Mack case the variance structure is generalised considerably from the existing literature. In the cross-classified case the model structure differs somewhat from the existing literature, and a comparison is made between the two. MAP estimators for the cross-classified case are often given by implicit equations that require numerical solution. Recursive formulas are given for these in the general case of error terms from the exponential dispersion family. The connection between the cross-classified case and Bornhuetter-Ferguson prediction is explored.
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Kuang, D., B. Nielsen, and J. P. Nielsen. "The geometric chain-ladder." Scandinavian Actuarial Journal 2015, no. 3 (2013): 278–300. http://dx.doi.org/10.1080/03461238.2013.821952.

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Dina Manolache, Aurora Elena. "Chain claims reserving methods in non-life insurance." Proceedings of the International Conference on Applied Statistics 1, no. 1 (2019): 216–25. http://dx.doi.org/10.2478/icas-2019-0019.

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Abstract Considering that the reliability of reserves valuation directly influences the financial strength of an insurance company, the main aim of this paper is to present a claims reserving estimation for a Romanian non-life insurer based on the most popular chain methods which are typically used in practice for the estimation of outstanding claims reserves in general insurance industry: Standard Chain Ladder and Munich Chain Ladder both on the claims incurred data and claims paid data. The tail development factors have been estimated based on the curve-fitting methods. The obvious advantage of these methods is represented by its simplicity of the practicality application. The results of the research under two chain claims reserving models reveal significant differences between the Standard Chain Ladder and Munich Chain Ladder with respect to the claims reserves level. Probably the Standard Chain Ladder based on paid method underestimates the outstanding loss liabilities and Standard Chain Ladder based on Incurred method overestimates the claims reserves. The claims reserves predictions under the Paid Munich Chain Ladder and Incurred Munich Chain Ladder are between the two Standard Chain Ladder outstanding loss liabilities estimates. The results of the tail extrapolation shown that the incorporation of the tail factors can have a significant impact on claims predictions.
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Hiabu, M., C. Margraf, M. D. Martínez-Miranda, and J. P. Nielsen. "The link between classical reserving and granular reserving through double chain ladder and its extensions." British Actuarial Journal 21, no. 01 (2015): 97–116. http://dx.doi.org/10.1017/s1357321715000288.

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AbstractThe relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the 1990s it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counterpart, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.
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Ajne, Björn. "Additivity of Chain-Ladder Projections." ASTIN Bulletin 24, no. 2 (1994): 311–18. http://dx.doi.org/10.2143/ast.24.2.2005072.

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AbstractIn this paper some results are given on the addivity of chain-ladder projections. Given two claims development triangles, when do their chain-ladder projections add up to the projections of the combined triangle, that is the triangle being the element-wise sum of the two given triangles?Necessary and sufficient conditions for equality are given. These are of a fairly simply form and are directly connected to the ordinary chain-ladder calculations. In addition, sufficient conditions of the same form are given for inequality between the combined projection vector and the sum of the two original projections vectors.
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Verrall, R. J. "Chain ladder and maximum likelihood." Journal of the Institute of Actuaries 118, no. 3 (1991): 489–99. http://dx.doi.org/10.1017/s0020268100019545.

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ABSTRACTThis paper derives second moments of estimates of the parameters in the chain ladder model. Thus, the so-called link ratios, and proportions of ultimate claims for each development year are considered. This enables confidence statements about the chain ladder parameters to be made with statistical rigour. The methods are illustrated using 6 sets of real data taken from the DTI returns.
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Röhr, Ancus. "CHAIN LADDER AND ERROR PROPAGATION." ASTIN Bulletin 46, no. 2 (2016): 293–330. http://dx.doi.org/10.1017/asb.2016.9.

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AbstractWe show how estimators for the chain ladder prediction error in Mack's (1993) distribution-free stochastic model can be derived using the error propagation formula. Our method allows for the treatment of the general case of the prediction error of the loss development result between two arbitrary future horizons. In the well-known special cases considered previously by Mack (1993) and Merz and Wüthrich (2008), our estimators coincide with theirs. However, the algebraic form in which we cast them is new, considerably more compact and more intuitive to understand. For example, in the classical case treated by Mack (1993), we show that the mean squared prediction error divided by the squared estimated ultimate loss can be written as ∑jû2j, where ûj measures the (relative) uncertainty around the jth development factor and the proportion of the estimated ultimate loss that it affects. The error propagation method also provides a natural split into process error and parameter error. Our proofs identify and exploit symmetries of “chain ladder processes” in a novel way. For the sake of wider practical applicability of the formulae derived, we allow for incomplete historical data and the exclusion of outliers in the triangles.
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Dissertations / Theses on the topic "Chain-ladder"

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Žváčková, Lenka. "Rozšířená metoda Chain Ladder s využitím kovariancí." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-15751.

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This diploma thesis deals with technical reserves in non-life insurance, in particular with provisions for future claim payments for damages that have occurred, but has not yet been reported to the insurance company. This type of provision is known by the acronym IBNR. After the introductory section containing a general introduction to the issue of claims reserving in non-life insurance different approaches to modeling of IBNR reserves are briefly presented. Subsequently, full attention is given to Chain-ladder method, which is most frequently used in the actuarial practise for the purpose of claims reserving. This method is then presented progressively from its simplest form of a simple computing algorithm followed by Mack's stochastic model to the last theoretical part of this part describing extended form of Chain-ladder method with relations between different groups of insurance portfolio included. In the very last section, all the lessons are demonstrated on real data to give readers an idea of how the process of claims reserving works is in the common actuarial practice.
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Johansson, Annelie. "Claims Reserving on Macro- and Micro-Level." Thesis, KTH, Matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-173113.

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Three methods for claims reserving are compared on two data sets. The first two methods are the commonly used chain ladder method that uses aggregated payments and the relatively new method, double chain ladder, that apart from the payments data also uses the number of reported claims. The third method is more advanced, data on micro-level is needed such as the reporting delay and the number of payment periods for every single claim. The two data sets that are used consist of claims with typically shorter and longer settlement time, respectively. The questions considered are if you can gain anything from using a method that is more advanced than the chain ladder method and if the gain differs from the two data sets. The methods are compared by simulating the reserves distributions as well as comparing the point estimates of the reserve with the real out-of-sample reserve. The results show that there is no gain in using the micro-level method considered. The double chain lad- der method on the other hand performs better than the chain ladder method. The difference between the two data sets is that the reserve in the data set with longer settlement times is harder to estimate, but no difference can be seen when it comes to method choice.<br>Tre reservsättningsmetoder jämförs på två dataset. De första två metoderna är den välkända chain ladder-metoden som använder sig av aggregerade utbetalningar samt den relativt nya metoden double chain ladder som förutom utbetalningarna använder sig av antalet anmälda skador. Den tredje metoden baseras på mikro-nivå och kräver information om varje enskild skada, såsom anmälningstid och antalet utbetalningsperioder. De två dataseten som används är ett som innehåller skador med typiskt kortare avvecklingstider och ett som innehåller skador med typiskt längre avvecklingstider. Frågorna som behandlas är om man vinner något på att använda en mer avancerad metod än chain ladder och om det skiljer sig åt mellan dataseten. Metoderna jämförs genom simulering av reserven, men också genom att jämföra punktskattningar med den verkliga reserven. Resultaten visar att man I detta fall inte vinner något på att använda mikro-metoden. Double chain ladder å andra sidan presterar bättre än chain ladder. Skillnaden mellan de två dataseten är att det är svårare att estimera reserven när avvecklingstiden är längre, men ingen skillnad ses när det gäller val av metod
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Sundberg, Victor. "Application and Bootstrapping of the Munich Chain Ladder Method." Thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-182136.

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Point estimates of the Standard Chain Ladder method (CLM) and of the more complex Munich Chain Ladder method (MCL) are compared to real data on 38 different datasets in order to evaluate if MCL produces better predictions on average with a dataset from an arbitrary insurance portfolio. MCL is also examined to determine if the future paid and incurred claims converge as time progresses. A bootstrap model based on MCL (BMCL) is examined in order to evaluate its possibility to estimate the probability density function (PDF) of future claims and observable claim development results (OCDR). The results show that the paid and incurred predictions by MCL converge. The results also show that when considering all datasets MCL produce on average better estimations than CLM with paid data but no improvement can be seen with incurred data. Further the results show that by considering a subset of datasets which fulfil certain criteria, or by only considering accident years after 1999 the percentage of datasets in which MCL produce superior estimations increases. When examining BMCL one finds that it can produce estimated PDFs of ultimate reserves and OCDRs, however the mean of estimate of ultimate reserves does not converge to the MCL estimates nor do the mean of the OCDRs converge to zero. In order to get the right convergence the estimated OCDR PDFs are centered and the mean of the BMCL estimated ultimate reserve is set to the MCL estimate by multiplication.<br>Punktskattningar gjorda med Standard Chain Ladder (CLM) och den mer komplexa Munich Chain Ladder-metoden (MCL) jämförs med verklig data för 38 olika dataset för att evaluera om MCL ger bättre prediktioner i genomsnitt än CLM för en godtycklig försäkringsportfölj. MCLs prediktioner undersöks också för att se om de betalda och de kända skadekostnaderna konvergerar. En bootstrapmodell baserad på MCL (BMCL) undersöks för att utvärdera om möjligheterna att estimera täthetsfunktionen (probability density function, PDF) av framtida skadekostnader och av ”observable claim development results (OCDR)”. Resultaten visar att MCLs estimerade betalda och kända skadekostnader konvergerar. Resultaten visar även att när man evaluerar alla dataseten så ger MCL i genomsnitt bättre prediktioner än CLM med betald data, men ingen förbättring kan ses med CLM med känd skadekostnadsdata. Vidare visar resultaten även att genom att bara titta på dataset som uppfyller vissa krav, eller genom att bara använda olycksår efter 1999, så ökar andelen dataset där MCL ger bättre prediktioner än CLM.Vid evaluering av BMCL ser man att den kan producera estimerade PDF:er för ultimo-reserver och OCDR:er, men att medelvärdet av ultimo-reserv prediktionerna från BMCL inte konvergerar mot MCL-prediktionerna och att medelvärdet av OCDR:erna inte konvergerar mot noll. För att få rätt konvergens så centreras OCDR PDF:erna och ultimo-reservernas medelvärden sätts till motsvarande MCL-prediktionens värde genom multiplikation.
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Martin, Peter. "Loss Reserving Chain Ladder Methods Applied to a Small Midwestern Insurance Company." Thesis, North Dakota State University, 2015. https://hdl.handle.net/10365/27866.

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Estimating future losses is integral to setting aside appropriate reserves in the insurance industry. This study analyzes different Chain Ladder reserving methods based on weighted-least square regression that consider different function of weights. These methods are tested on 78 NAIC fully developed loss triangles. While the CRE Chain Ladder method is selected based on its performance, this method does not work well for a small number of NAIC companies that may have erratic changes in their loss trends. For these outliers, two other methods were explored for the early development years; the nearest neighbor technique and mixture of linear regressions. A recommendation is then made to a small Midwestern insurance company on the best methodology to use for estimating the loss reserves based on the actual data provided. These results can be useful to any other insurance company currently using Chain Ladder methods in loss reserving practices.
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Kuang, Di. "The chain ladder method and its extensions for forecasting reserves in general insurance." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.531972.

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Mazuelos, Vizcarra Gisella Gabriela. "Modelos Chain Ladder estocásticos y aplicaciones al cálculo de reservas en compañías de seguros." Master's thesis, Pontificia Universidad Católica del Perú, 2013. http://tesis.pucp.edu.pe/repositorio/handle/123456789/6176.

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This document is intented to deepen the study of univariate and multivariate Chain Ladder methods for estimating reserves in an insurance company. It presents from a theoretical and applicative perspective both the univariate deterministic and stochastic Chain Ladder methods. Although, the first is the most used method by insurance companies due to its simplicity and lack of probabilistic assumptions, the second, proposed by Mack (1993), allows the construction of confidence intervals for the estimated reserves, which is invaluable for researchers. We also develop the General Multivariate Chain Ladder model, which has the basic premise to analyze the possible relationship that may exist between different development triangles, thus providing another tool to improve inferences and predictions of reserves. These methods have been developed and applied to a database of 3 types of health insurance, thus showing the advantages and disadvantages of each of them in different scenarios and providing various tools for decision making in meeting the future obligations of insurance companies.<br>El presente documento tiene por objetivo profundizar en el estudio de los m´etodos univariados y multivariados del modelo Chain Ladder para la estimaci´on de las reservas de una compa˜n´ıa de seguros. Se presenta de manera te´orica y aplicativa tanto los m´etodos univariados Chain Ladder determin´ıstico como Chain Ladder estoc´astico. Si bien el primero de estos m´etodos es el m´as utilizado por las compa˜n´ıas de seguro dada su simplicidad de c´alculo y carencia de supuestos probabil´ısticos, el segundo, propuesto por Mack (1993), permite la construcci´on de intervalos de confianza para las reservas, lo cu´al es de invalorable ayuda para los investigadores. Asimismo, desarrollamos el modelo General Multivariado Chain Ladder, el cual tiene como premisa b´asica analizar la posible relaci´on que pueda existir entre diversos tri´angulos de desarrollo, dotando as´ı de otra herramienta para mejorar las inferencias y predicciones de las reservas. Estos m´etodos han sido desarrollados y aplicados sobre la base de datos de 3 tipos de seguros de salud, mostrando as´ı las ventajas y desventajas de cada uno de ellos en diferentes escenarios y proporcionando distintos instrumentos para la toma de decisiones relacionados en el cumplimiento de las obligaciones futuras de las compa˜nias de seguros.<br>Tesis
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Vild, Jiří. "Technické rezervy v neživotním pojištění." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-19197.

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One of the main and crucial activities of an insurance company is to determine amount of technical reserves to be generated. If the insurance company performs in the non-life insurance branch, it focuses first of all on loss reserve which is generated to settle debts coming from insurance claims. To set the proper amount of this reserve, especially of the reserve on incurred but not reported losses (IBNR), mathematical and statistical methods are used. This thesis introduces one of the most used methods which is the chain ladder method. It presents the first chain ladder deterministic model then moves to its stochastic extension in a form of Mack's model and finally gets to the Munich chain ladder model, which takes into calculations not only data on losses paid but also losses incurred. In the theoretical part both these models (standard Mack's chain ladder and Munich chain ladder) are presented both separately and in a common context so that later in the analytical section they could be demonstrated on real data.
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Sousa, Nilsa Fonseca. "Método de Bootstrap e teoria da credibilidade na estimativa das provisões para sinistros." Master's thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/5971.

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Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações, no ramo Actuariado, Estatística e Investigação Operacional<br>A adequação das provisões técnicas é objecto de estudo por parte das próprias Seguradoras. A não constituição de provisões adequadas pode comprometer a solvência das mesmas. De entre os vários tipos de provisões, as provisões para sinistros têm uma grande relevância nas contas dos ramos não vida. Existem vários métodos, tanto determinísticos como estocásticos, para a sua determinação. Dos modelos determinísticos,o modelo de Chain Ladder é o mais conhecido e utilizado. No entanto, a aplicação de modelos estocásticos tem vindo a aumentar. A principal vantagem é a obtenção de intervalos de confiança para a estimativa da provisão. No presente trabalho pretende-se aplicar a Teoria da Credibilidade e o método de Bootstrap ao cálculo de provisões para sinistros do ramo automóvel com respectiva comparação de resultados obtidos.
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COSTA, LEONARDO HENRIQUE. "MODELING IBNR CLAIMS WITH TAIL EFFECT: EXTENDED CHAIN LADDER, HETEROCEDASTIC LINEAR REGRESSION MODELS AND LINEAR STATE SPACE MODELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=15850@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>Este trabalho utiliza três metodologias para modelagem de sinistros IBNR apresentados no formato do triângulo de runoff com cauda, e verifica, por meio de quatro exercícios empíricos com dados reais, se existe uma abordagem estatisticamente mais eficaz. A primeira metodologia se baseia no método do chain ladder clássico, com uma extensão de cálculo de reserva para ano de calendário. A segunda metodologia baseia-se em modelos de regressão linear com heterocedasticidade, sob o arranjo usual do triângulo via duplo-índice. A terceira insere-se no arcabouço dos modelos de espaço de estado lineares e do filtro de Kalman, considerando, desta vez, a ordenação por linhas do triângulo de Atherino et al. (2010). Para todas as abordagens, efetivam-se derivações teóricas e implementações computacionais tanto dos cálculos de reservas IBNR totais e parciais, resultantes dos modelos estimados, quanto dos correspondentes erros médios quadráticos teóricos. Como conclusões desta Dissertação, citam-se: (i) apesar de superiores ao chain ladder, nenhuma das outras duas abordagens se destaca sistematicamente em relação à outra; (ii) a adoção do efeito cauda se mostrou computacional e tecnicamente viável; e (iii) há fatos estilizados nos dados, modelados sob as três abordagens, que possibilitariam a confecção de softwares de estimação de reserva.<br>This work makes use of three methodologies for modeling IBNR data arranged in the runoff triangle with a tail effect, and evaluates their performances in four empirical examples. The first methodology is the traditional chain ladder, duly extended to calculate a reserve corresponding to the calendar year. The second methodology remains on linear regression models with heteroscedastic errors, under the well-established double index notation of the triangle. The third methodology uses the linear state space modeling and the theory of the Kalman filter, adopting, this time, the row-wise ordering proposed by Atherino et al. (2010). For each approach, theoretical results and numerical implementations are obtained, where both the punctual IBNR reserve estimators and their corresponding theoretical mean square errors are considered. The main conclusions from this Dissertation are: (i) even thought proving to be superior to the chain ladder, none of the remaining two approaches seems to outperform the other; (ii) the adding of a tail effect does not entail major theoretical and/or computational problems; and (iii) the approaches have uncovered stylized facts that would enable the planning of softwares for IBNR reserve estimation.
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Sloma, Przemyslaw. "Contribution to the weak convergence of empirical copula process : contribution to the stochastic claims reserving in general insurance." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066563/document.

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Dans la première partie de la thèse, nous nous intéressons à la convergence faible du processus empirique pondéré des copules. Nous fournissons la condition suffisante pour que cette convergence ait lieu vers un processus Gaussien limite. Nos résultats sont obtenus dans un espace de Banach L^p. Nous donnons des applications statistiques de ces résultats aux tests d'adéquation (tests of goodness of fit) pour les copules. Une attention spéciale est portée aux tests basées sur des statistiques de type Cramér-von Mises.Dans un second temps, nous étudions le problème de provisionnement stochastique pour une compagnie d'assurance non-vie. Les méthodes stochastiques sont utilisées afin d'évaluer la variabilité des réserves. Le point de départ pour cette thèse est une incohérence entre les méthodes utilisées en pratique et celles publiées dans la littérature. Pour remédier à cela, nous présentons un outil général de provisionnement stochastique à horizon ultime (Chapitre 3) et à un an (Chapitre 4), basé sur la méthode Chain Ladder<br>The aim of this thesis is twofold. First, we concentrate on the study of weak convergence of weighted empirical copula processes. We provide sufficient conditions for this convergence to hold to a limiting Gaussian process. Our results are obtained in the framework of convergence in the Banach space $L^{p}$ ($1\leq p &lt;\infty $). Statistical applications to goodness of fit (GOF) tests for copulas are given to illustrate these results. We pay special attention to GOF tests based on Cramér-von Mises type statistics. Second, we discuss the problem of stochastic claims reserving in general non-life insurance. Stochastic models are needed in order to assess the variability of the claims reserve. The starting point of this thesis is an observed inconsistency between the approaches used in practice and that suggested in the literature. To fill this gap, we present a general tool for measuring the uncertainty of reserves in the framework of ultimate (Chapter 3) and one-year time horizon (Chapter 4), based on the Chain-Ladder method
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Books on the topic "Chain-ladder"

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Leathers, Kuntz Marion, and Kuntz Paul Grimley 1915-, eds. Jacob's ladder and the tree of life: Concepts of hierarchy and the Great chain of being. P. Lang, 1988.

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Leathers, Kuntz Marion, and Kuntz Paul Grimley 1915-, eds. Jacob's ladder and the tree of life: Concepts of hierarchy and the great chain of being. P. Lang, 1987.

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(Editor), Marion Leathers Kuntz, and Paul Grimley Kuntz (Editor), eds. Jacob's Ladder and the Tree of Life: Concepts of Hierarchy and the Great Chain of Being (American University Studies Series V, Philosophy). Peter Lang Pub Inc, 1987.

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Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is necessary to introduce non-correlation decoupling procedures involving the Hartree and Hartree-Fock approximations for G2 in the G1 equation; and a similar factorization “ansatz” for G3 in the G2 equation, resulting in the Sum of Ladder Diagrams integral equation for G2, with multiple Born iterates and finite collisional lifetimes. Similar treatment of the G11-equation for the joint propagation of one-electron and one-hole subject to mutual Coulomb attraction leads to bound electron-hole exciton states having a discrete hydrogen like spectrum of energy eigenstates. Its role in single-particle propagation is also discussed in terms of one-electron self-energy Σ‎ and the T-matrix
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Book chapters on the topic "Chain-ladder"

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Taylor, Greg. "Stochastic Chain Ladder." In Loss Reserving. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4583-5_7.

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Schmidt, Klaus D. "Schadenreservierung:Grundlagen und chain–ladder." In Springer-Lehrbuch. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01176-4_14.

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Gao, Guangyuan. "Bayesian Chain Ladder Models." In Bayesian Claims Reserving Methods in Non-life Insurance with Stan. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-3609-6_4.

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Schmidt, Klaus D. "Munich Chain Ladder Method." In EAA Series. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30056-6_27.

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Schmidt, Klaus D. "Chain Ladder Method (Basics)." In EAA Series. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30056-6_6.

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Hess, Klaus Th, Klaus D. Schmidt, and Anja Schnaus. "Chain Ladder Method (Models)." In EAA Series. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30056-6_7.

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Schmidt, Klaus D. "Chain Ladder Method (Prediction Error)." In EAA Series. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30056-6_8.

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Chen, S. H., T. L. Lin, and C. F. Wu. "SANS Study of Structure, Growth, and Polydispersity of Short-Chain Lecithin Micellar Systems. A Ladder Model Analysis." In Springer Proceedings in Physics. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83202-4_35.

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"Chain-Ladder Models." In Stochastic Claims Reserving Methods in Insurance. John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119206262.ch3.

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"Selected Topics I: Chain-Ladder Methods." In Stochastic Claims Reserving Methods in Insurance. John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119206262.ch9.

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Conference papers on the topic "Chain-ladder"

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Heberle, Jochen, and Anne Thomas. "Combining chain-ladder claims reserving with fuzzy numbers." In 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). IEEE, 2013. http://dx.doi.org/10.1109/ifsa-nafips.2013.6608383.

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Raeva, Elitsa, Velizar Pavlov, and Simona Georgieva. "Claim reserving estimation by using the chain ladder method." In SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040192.

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Brzezicki, W., Adolfo Avella, and Ferdinando Mancini. "Quantum compass model on a chain, ladder and finite square clusters." In LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XIV: Fourteenth Training Course in the Physics of Strongly Correlated Systems. AIP, 2010. http://dx.doi.org/10.1063/1.3518903.

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Suwardi, Desnu Anggara, and Yogo Purwono. "The Analysis of Motor Vehicle Insurance Claim Reserve Using Robust Chain Ladder." In 5th Global Conference on Business, Management and Entrepreneurship (GCBME 2020). Atlantis Press, 2021. http://dx.doi.org/10.2991/aebmr.k.210831.031.

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Yecheng Zhang, Guohai Liu, Rongbiao Zhang, and Chunyan Zhang. "Cycle chain ladder deceleration control method research based on permanent magnet synchronous generator." In 2010 IEEE International Conference on Information Theory and Information Security (ICITIS). IEEE, 2010. http://dx.doi.org/10.1109/icitis.2010.5689625.

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Prins, P., F. C. Grozema, J. M. Schins, S. Patil, U. Scherf, and L. D. A. Siebbeles. "High intra-chain hole mobility on molecular wires of ladder type poly(p-phenylenes)." In SPIE Optics + Photonics, edited by Zhenan Bao and David J. Gundlach. SPIE, 2006. http://dx.doi.org/10.1117/12.678257.

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Raeva, Elitsa, and Velizar Pavlov. "Inflation as a factor in the chain ladder method for estimating outstanding claims reserves." In EIGHTH INTERNATIONAL CONFERENCE NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0083769.

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Zhang, Liaoliao. "An Empirical Study of Comprehensive Ladder Task Chain Model in Independent Colleges' Business English Writing Course." In International Conference on Education, Management and Computing Technology (ICEMCT-16). Atlantis Press, 2016. http://dx.doi.org/10.2991/icemct-16.2016.278.

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Sivanathan, Aparajithan, Mohamed Abdel-Wahab, Frederic Bosche, and Theodore Lim. "Towards a Cyber-Physical Gaming System for Training in the Construction and Engineering Industry." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34930.

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Abstract:
Introducing serious gaming systems (SGS) has the potential to enhance trainee experience and performance across the construction industry and its supply chain, such as mechanical engineering services. SGS as an ‘enabler’ in architectural engineering has received limited research in its role to assess and enhance the performance of its workforce. In a personnel high-risk environment, improving training standards to eliminate or reduce health and safety risks, in addition to providing an understanding of workers’ ergonomics, ensures sustainability of both the project and its workforce. This paper presents an activity tracking and feedback system that captures the physical activity of a construction worker climbing a ladder. Climbing is captured with a 3D motion capture system and processed in real-time to identify potential areas of underperformance. A simple and representative scoring method was established as a reporting method (game statistics) for giving feedback about the correctness of the activity. It can nonetheless be tuned to characterise and adjust to various complexity levels in-line with the required training standards. Furthermore, the motion data and feedback information are fed into a virtual gaming environment enabling the real-time visualisation of the trainee’s motion and experiential learning of the performance through visual and audio feedback. The gaming concepts are employed here with multiple purposes, particularly for accelerating and facilitating the learning process of the trainee. In addition to the 3D motion capturing system, this paper outlines and tests a proposed serious cyber-physical gaming system that incorporates wearable technologies that has the potential to support both construction training and practice.
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Reports on the topic "Chain-ladder"

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Anzolin, Guendalina. Productive Development Policies in the Mining Value Chain: Policy Opportunity and Alignment. Inter-American Development Bank, 2021. http://dx.doi.org/10.18235/0003886.

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Natural resources are an important source for development, and Latin America is one of the regions with the highest endowment. This calls for a reconsideration of resource-based development. Ambitious countries are moving toward high-value activities and more diversified economies to continue moving up the development ladder. In this sense, the resurgence of industrial policy can correct market failures and lead to the implementation of mission-oriented policies. This document analyzes opportunities to design and implement integrated policies through a revised taxonomy of mining-related policies, applying it to Australia, South Africa, and Chile. The mining sector has been a fertile field, characterized by high technology niches, growth, and innovation. Demand and supply policies can shape the path for development within the sector and across the economy due to the potential of vertical and horizontal linkages.
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