Applying copula models to individual claim loss reserving methods

Zhao, Xiaobing; Zhou, Xian

doi:10.1016/j.insmatheco.2009.11.001

Cited by 51 publications

(33 citation statements)

References 58 publications

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“…Recently, Larsen (2007) revisited the work of Norberg, Haastrup and Arjas with a small case-study. Zhao et al (2009) and Zhao and Zhou (2010) present a model for individual claims development using (semi-parametric) techniques from survival analysis and copula methods. However, a case study is lacking in their work.…”

Section: Introductionmentioning

confidence: 99%

Micro-Level Stochastic Loss Reserving

Antonio

Plat

2010

SSRN Journal

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Abstract1 To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run-off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as 'micro-level data'. We investigate whether the use of such micro-level claim data can improve the reserving process. A realistic micro-level data set on liability claims (material and injury) from a European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an outof-sample prediction exercise we show that the micro-level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case-study reserve calculations based on the micro-level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way.

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Section: Introductionmentioning

confidence: 99%

Micro-Level Stochastic Loss Reserving

Antonio

Plat

2010

SSRN Journal

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“…With an explanatory variable highly correlated with the response variable, results obtained with Model D and E are very close. As claimed by Proposition 6 and Equation (14), an explanatory variable highly correlated with the response variable will decrease the value of √ MSEP, and lowers the threshold above which the micro-level model is more accurate than the macro-level one.…”

Section: Illustration and Discussionmentioning

confidence: 89%

“…As mentioned in [12], these methods have not (yet) found great popularity in practice, since they are more difficult to apply. Nevertheless, several papers address that issue, with several stochastic processes to model the dynamics of payments, such as [13]-extended in [14,15] or [16], and more recently [17] and [18].…”

Section: Macro and Micro Methodsmentioning

confidence: 99%

Macro vs. Micro Methods in Non-Life Claims Reserving (an Econometric Perspective)

Charpentier

Pigeon

2016

Risks

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Traditionally, actuaries have used run-off triangles to estimate reserve ("macro" models, on aggregated data). However, it is possible to model payments related to individual claims. If those models provide similar estimations, we investigate uncertainty related to reserves with "macro" and "micro" models. We study theoretical properties of econometric models (Gaussian, Poisson and quasi-Poisson) on individual data, and clustered data. Finally, applications in claims reserving are considered.

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“…In order to estimate the loss reserves for incurred but not reported (IBNR) claims through individual claim loss models instead of aggregated claim loss models, [23] use the semi-survival copula and the semi-competing risk copula to model the dependence between the event times with delays in the individual claim loss model. The performances of their proposed methods are evaluated through simulation.…”

Section: Modelling Of Claim Sizementioning

confidence: 99%

“…It was first introduced by [53] and has attracted considerable attention in theoretical and application aspects in recent years. In insurance data analysis, copula-based approaches are used to model the dependence between different claim types [10,54], between accident date and reported date [23], between policy coverage and number of claims [17,18,55], between claim counts in successive periods [12,13], between claims in different business lines [56,57], between number 398 of claims and average claim size [4], and between time-to-claim and claim size [8].…”

Section: Dependence In Warranty Data Analysismentioning

confidence: 99%

An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

Luo¹,

Wu²

2016

ENG

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Warranty shares similarities with insurance in many aspects. Research on insurance data analysis has attracted much more attention than on warranty data analysis. This paper provides a general comparison between warranty and insurance in terms of their coverages, policies and data collection. It then reviews existing approaches to insurance data analysis with regard to modelling of claim frequency, modelling of claim size and policy pricing. Some recent patents relating statistical models are also discussed. The paper concludes with suggestions for improving warranty data analysis.

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Applying copula models to individual claim loss reserving methods

Cited by 51 publications

References 58 publications

Micro-Level Stochastic Loss Reserving

Micro-Level Stochastic Loss Reserving

Macro vs. Micro Methods in Non-Life Claims Reserving (an Econometric Perspective)

An Overview of Approaches to Insurance Data Analysis and Suggestions for Warranty Data Analysis

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