Exponential Behavior in the Presence of Dependence in Risk Theory

Albrecher, Hansjörg; Teugels, Jozef L.

doi:10.1239/jap/1143936258

Cited by 145 publications

(88 citation statements)

References 16 publications

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“…This work is extended within the class of renewal risk models in Tang (2005aTang ( , 2007 and Wang (2008). Asymptotic formulas for finite/infinite time ruin probabilities with a certain dependence structure between claim sizes and inter-claim times are also obtained by Albrecher and Teugels (2006) for which the evolution of the surplus U δ (t) is given by…”

Section: Ruin Probabilitymentioning

confidence: 99%

“…Using random walk techniques, Albrecher and Teugels (2006) derive explicit exponential estimates for infinite and finite time ruin probabilities under a dependence structure described by a copula, when the claim sizes are light tailed. Another type of dependence structure that falls under our assumption is considered by Boudreault et al (2006).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Ruin Probabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Asimit

Badescu

2010

Scandinavian Actuarial Journal

114

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“…[7,Ch.III.2]), risk processes of that type have a counterpart in workload models of queueing theory, and a similar semi-Markovian structure was considered in [1] in a queueing context. In [5] it was proposed to assume that (A k , B k ) are i.i.d. pairs of positive random variables, but for each k, A k and B k may be dependent.…”

Section: Introductionmentioning

confidence: 99%

“…In [8] an explicit expression for ψ(x) could be obtained for a particular type of dependence between A k and B k . In [14], another explicit dependence structure in the framework of [5] was considered: if A k < a, then B k is distributed according to B (1) , otherwise according to B (2) , where a is a fixed threshold. It could be shown in [14] that the ruin probability for this model has a remarkably simple form * hansjoerg.…”

Section: Introductionmentioning

confidence: 99%

On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

Albrecher¹,

Boxma²,

Ivanovs³

2014

J. Appl. Probab.

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In this note we provide a simple alternative derivation of an explicit formula of Kwan and Yang [14] for the probability of ruin in a risk model with a certain dependence between general claim inter-occurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence.

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“…Their model depicts common sense that when a certain kind of catastrophe is big enough, people will pay more attention to it and so the time until the next occurrence is longer. [2] and [4] considered a particular dependence structure among the inter-claim time and subsequent claim size. Furthermore, [16] have studied risk models with dependence between inter-claim times and claim sizes.…”

Section: Introductionmentioning

confidence: 99%

On the probability of ruin in the compound Poisson risk model with potentially delayed claims

Xie¹,

Zou²,

Gao

2012

Arab. J. Math.

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In this paper, we consider the compound Poisson risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim with a certain probability and the occurrence of a by-claim may be delayed depending on associated main claim amount. Using Rouché's theorem, both of the survival probability with zero initial surplus and the Laplace transform of the survival probability are obtained from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. An exact representation for the solution of this equation is derived through an associated compound geometric distribution. For exponential claim sizes, we present an explicit formula for the survival probability. We also illustrate the influence of model parameters in the dependent risk model on the survival probability by numerical examples. Mathematics Subject Classification 60J65 · 91B30

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Exponential Behavior in the Presence of Dependence in Risk Theory

Cited by 145 publications

References 16 publications

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

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

On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

On the probability of ruin in the compound Poisson risk model with potentially delayed claims

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