Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation

Cossette, Hélène; Côté, Marie‐Pier; Marceau, Étienne; Moutanabbir, Khouzeima

doi:10.1016/j.insmatheco.2013.03.006

Cited by 63 publications

(52 citation statements)

References 20 publications

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“…Within the actuarial literature, several applications of copulas to insurance framework have been dealt with (Frees and Valdez, 1998;Frees and Wang, 2006;Eling and Toplek, 2009;Zhao and Zhou, 2010;Shi and Frees, 2011;Cossette et al, 2013;Fang and Madsenb, 2013). The recent advances for high-dimensional copula models tend towards hierarchical structures based on the building blocks, known as pair copula construction (PCC).…”

Section: Asian Development Policy Reviewmentioning

confidence: 99%

“…Conceptually, the risk capital is defined as the capital cushion against unexpected losses in a worst-case scenario calculated using the risk measure VaR at a specified confidence α over a given time period. Nevertheless, several authors have criticized the use of VaR to compute the minimum capital requirement and have recommended the use of an alternative measure, namely the TailVaR (Kaas et al, 2009;Goovaerts et al, 2010;Cossette et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

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A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas

Mejdoub¹,

Arab²

2017

Asian Development Policy Review

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Article HistoryThis paper deals with the risks aggregation issue and adequate risk capital modeling within a multivariate setting. Focusing on the non-life insurance risk module, we examine the sensitivity of capital requirement to the dependence among risks for a multi-line Tunisian insurance firm. Such a context entails a nonlinear dependence of risks problem whose resolution may be intended by means of multivariate copulas. The relevant analysis relies profoundly on the dependence modeling by the means of vine copulas which are a flexible technique to model multivariate distributions constructed using a cascade of bivariate copulas. Under various confidence levels in VaR and TailVaR, the reached findings reveal the advantages of D-Vine copula in modeling inhomogeneous structures of dependency due to its flexibility of use in a simulation context. Practitioners and regulators can explore our conclusions for the assessment of risk capital under Solvency 2, which is based on stochastic models.Contribution/ Originality: This study uses new methodology based on CD-vine copulas estimation to investigate the sensitivity of solvency capital requirement to the dependence pattern between the losses derived from non-life business lines of a Tunisian insurance company.

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Section: Asian Development Policy Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas

Mejdoub¹,

Arab²

2017

Asian Development Policy Review

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“…Under the Euler principle the allocation for each one of the portfolio's constituents can be calculated through an expectation conditional on a rare event. Even though, in general, these expectations are not available in closed form, some exceptions exist, such as the multivariate Gaussian model, first discussed in this context in and extended to the case of multivariate elliptical distributions in Landsman and Valdez (2003) and ; the multivariate gamma model of Furman and Landsman (2005); the combination of the Farlie-Gumbel-Morgenstern (FGM) copula and (mixtures of) exponential marginals from Bargès et al (2009) or (mixtures of) Erlang marginals Cossette et al (2013); and the multivariate Pareto-II from Asimit et al (2013).…”

Section: Introductionmentioning

confidence: 99%

A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

2018

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“…Even though, in general, these expectations are not available in closed form, some exceptions exist, such as the multivariate Gaussian model, first discussed in this context in Panjer (2001) and extended to the case of multivariate elliptical distributions in Landsman and Valdez (2003) and Dhaene et al (2008); the multivariate gamma model of Furman and Landsman (2005); the combination of the Farlie-Gumbel-Morgenstern (FGM) copula and (mixtures of) exponential marginals from Bargès et al (2009) or (mixtures of) Erlang marginals Cossette et al (2013); and the multivariate Pareto-II from Asimit et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

Peters

Targino

Wüthrich

2017

Risks

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Abstract:The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method to calculate capital allocations for a general insurance company is developed, with a focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed.

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Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation

Cited by 63 publications

References 20 publications

A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas

A Multivariate Analysis for Risk Capital Estimation in Insurance Industry: Vine Copulas

A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

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