On a risk model with dependence between interclaim arrivals and claim sizes

Boudreault, Mathieu; Cossette, Hélène; Landriault, David; Marceau, Étienne

doi:10.1080/03461230600992266

Cited by 151 publications

(211 citation statements)

References 24 publications

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“…Some research has also been performed beyond the Sparre Andersen assumption of independence of the times between consecutive claim arrivals. Thus, risk models in which an appropriate dependence structure is imposed on the claim inter-arrival times and claim sizes, has been considered in [1], assuming the premium income function, h(t) = u + ct, and also in [4].…”

Section: Introductionmentioning

confidence: 99%

Finite time non-ruin probability for Erlang claim inter-arrivals and continuous inter-dependent claim amounts

Ignatov¹,

Kaishev

2011

Stochastics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. A closed form expression, in terms of some functions which we call exponential Appell polynomials, for the probability of non-ruin of an insurance company, in a finite-time interval is derived, assuming independent, non-identically Erlang distributed claim inter-arrival times, Permanent repository link. ., any continuous joint distribution of the claim amounts and any non-negative, non-decreasing real function, representing its premium income. In the special case when τ i ∼ Erlang (g i , λ) , i = 1, 2, . . . it is shown that our main result yields a formula for the probability of non-ruin expressed in terms of the classical Appell polynomials. We give another special case of our non-ruin probability formula for. ., i.e., when the inter-arrival times are non-identically exponentially distributed and also show that it coincides with the formula for Poisson claim arrivals, given in [18], when τ i ∼ Erlang(1, λ), i = 1, 2, . . .. The main result is extended further to a risk model in which inter-arrival times are dependent random variables, obtained by randomizing the Erlang shape or/and rate parameters. We give also some useful auxiliary results which characterize and express explicitly (and recurrently) the exponential Appell polynomials which appear in our finite time non-ruin probability formulae.

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Section: Introductionmentioning

confidence: 99%

Finite time non-ruin probability for Erlang claim inter-arrivals and continuous inter-dependent claim amounts

Ignatov¹,

Kaishev

2011

Stochastics

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“…4 We point out that when q = 1, the compound Poisson risk model with potentially delayed claims is equivalent to the dependent risk model studied by [17]. To see that, letting q = 1 in (3.2), we have…”

Section: )mentioning

confidence: 99%

“…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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“…Another type of dependence structure that falls under our assumption is considered by Boudreault et al (2006). The present work is not meant to be an exhaustive treatment on all possible dependence structures, but rather an attempt to assess the impact of dependence over independence, via asymptotic tail probability evaluation.…”

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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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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On a risk model with dependence between interclaim arrivals and claim sizes

Cited by 151 publications

References 24 publications

Finite time non-ruin probability for Erlang claim inter-arrivals and continuous inter-dependent claim amounts

Finite time non-ruin probability for Erlang claim inter-arrivals and continuous inter-dependent claim amounts

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

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

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