Analysis of the Expected Shortfall of Aggregate Dependent Risks

Alink, Stan; Löwe, Matthias; Wüthrich, Mario V.

doi:10.2143/ast.35.1.583164

Cited by 22 publications

(16 citation statements)

References 9 publications

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“…Following Wüthrich (2003) and Alink et al (2004Alink et al ( , 2005, this paper considers the behavior of P(S > t) for large values of t when the claims exhibit extreme-value behavior and are dependent. As shown by these authors, the problem is of relevance to risk managers and actuaries who wish to estimate, e.g., the Value-at-Risk (VaR) associated with S.…”

Section: Introductionmentioning

confidence: 99%

“…I or not. In their papers, Wüthrich (2003) and Alink et al (2004Alink et al ( , 2005 consider this question in the special case where D is Archimedean, which means (see, e.g., MacKay 1986 or Nelsen 1999, Chapter 4) that there exists a func-…”

Section: Introductionmentioning

confidence: 99%

“…Expressions for D are derived by Wüthrich (2003) and Alink et al (2004Alink et al ( , 2005 under conditions which amount to the assumption that ƒ(1/t) ! RV(a) and the common margin F belongs to the Fréchet domain of attraction.…”

Section: Introductionmentioning

confidence: 99%

“…

ABSTRACTThe tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al (2004Alink et al ( , 2005 in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory.

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confidence: 99%

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On the Tail Behavior of Sums of Dependent Risks

2006

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The tail behavior of sums of dependent risks was considered by Wüthrich (2003) and by Alink et al. (2004Alink et al. ( , 2005 in the case where the variables are exchangeable and connected through an Archimedean copula model. It is shown here how their result can be extended to a broader class of dependence structures using multivariate extreme-value theory. An explicit form is given for the asymptotic probability of extremal events, and the behavior of the latter is studied as a function of the indices of regular variation of both the copula and the common distribution of the risks.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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On the Tail Behavior of Sums of Dependent Risks

2006

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“…The proof follows in a similar manner to the one of Theorem 3.1 of Alink et al (2005). Due to (7) and (11), F ∈ S M DA(Λ) implies that the df of S 0 (T ) belongs to M DA(Λ) and furthermore…”

Section: Risk Measuresmentioning

confidence: 72%

Extremes on the discounted aggregate claims in a time dependent risk model

Asimit

Badescu

2010

Scandinavian Actuarial Journal

114

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This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables. Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed random variables. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims.A simulation study is performed in order to validate the results obtained in the free interest risk model.

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Asymptotic finite‐time ruin probabilities for a class of path‐dependent heavy‐tailed claim amounts using Poisson spacings

Biard¹,

Lefèvre²,

Loisel³

et al. 2010

Appl Stoch Models Bus & Ind

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In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter-dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind, where each claim amount depends on the previous claim inter-arrival time, or on past claim inter-arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite-time ruin probabilities of the company when the claim sizes have a heavy-tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process.

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Analysis of the Expected Shortfall of Aggregate Dependent Risks

Cited by 22 publications

References 9 publications

On the Tail Behavior of Sums of Dependent Risks

On the Tail Behavior of Sums of Dependent Risks

Extremes on the discounted aggregate claims in a time dependent risk model

Asymptotic finite‐time ruin probabilities for a class of path‐dependent heavy‐tailed claim amounts using Poisson spacings

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