On the compound Poisson risk model with dependence based on a generalized Farlie–Gumbel–Morgenstern copula

Cossette, Hélène; Marceau, Étienne; Marri, Fouad

doi:10.1016/j.insmatheco.2008.08.009

Cited by 108 publications

(41 citation statements)

References 10 publications

(13 reference statements)

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“…Boudreault et al (2006) considered the dependent Poisson risk model with K (t) = 1−e −λt and P t (y) = e −βt P (1) (y) + (1 − e −βt )P (2) (y) where P (1) (y) and P (2) (y) are ''usual'' and ''severe'' claim size distribution functions, respectively. Cossette et al (2008) also used K (t) = 1 − e −λt , but with P t (y) = C (P(y), 1 − e −λt )/(1 − e −λt ), where C (u, v) is a generalized Farlie-Gumbel-Morgenstern copula. Badescu et al (2009) assumed a bivariate phase-type distribution for (V , Y ), and Albrecher and Teugels (2006) examined asymptotics for ruin probabilities for the present model.…”

Section: Introductionmentioning

confidence: 99%

Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

Cheung

Landriault

Willmot

et al. 2010

Insurance: Mathematics and Economics

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Section: Introductionmentioning

confidence: 99%

Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

Cheung

Landriault

Willmot

et al. 2010

Insurance: Mathematics and Economics

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“…For s on the imaginary axis, i.e., for Re(s) = 0, and for δ > 0, similar to Cossette et al (2008), we have…”

Section: Analysis Of a Generalized Lundberg Equationmentioning

confidence: 75%

“…Meng et al (2008) studied the ruin probability for a risk model with a dependent setting where the time between the two claim occurrences determines the distribution of the next claim. Cossette et al (2008Cossette et al ( , 2010 In this paper, we consider a renewal or Sparre Andersen risk process with dependence between the claim size and the interclaim time, based on the Farlie -Gumbel -Morgenstern copula. We assume that the interclaim times are distributed according to an Erlang(n) distribution.…”

Section: Introductionmentioning

confidence: 99%

On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula

Chadjiconstantinidis

Vrontos

2012

Scandinavian Actuarial Journal

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In this paper we consider an extension to the renewal or Sparre Andersen risk process by introducing a dependence structure between the claim sizes and the interclaim times through a Farlie-GumbelMorgenstern copula proposed by Journal, 2010, 3, 221-245]. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalized Lundberg equation, the Laplace transform of the expected discounted penalty function is derived and a detailed analysis of the Gerber -Shiu function is given when the initial surplus is zero. It is proved that this function satisfies a defective renewal equation and its solution is given through the compound geometric tail representation of the Laplace transform of the time to ruin. Explicit expressions for the discounted joint and marginal distribution functions of the surplus prior to the time of ruin and the deficit at the time of ruin are derived. Finally, for exponential claim sizes explicit expressions and numerical examples for the ruin probability and the Laplace transform of the time to ruin are given.

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“…Trivially, if θ = 0 then (1.3) describes a joint distribution function of two independent random variables. We refer the reader to Kotz et al (2000) for a general account on FGM distribution functions, and to Tang and Vernic (2007) and Cossette et al (2008) for applications of FGM distribution functions to risk theory. First, under the assumption that F in (1.3) is a subexponential distribution function while G fulfills some constraints in order for the product convolution of F and G to be a subexponential distribution function too, we derive a general asymptotic formula for the ruin probability ψ(x; n).…”

Section: (X Y) = F (X)g(y)(1 + θ F (X)g(y))mentioning

confidence: 99%

The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks

Chen

2011

J. Appl. Probab.

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Consider a discrete-time insurance risk model. Within period i, the net insurance loss is denoted by a real-valued random variable X i . The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factor Y i from time i to time i − 1. Assume that (X i , Y i ), i ∈ N, form a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functions F and G. When F is subexponential and G fulfills some constraints in order for the product convolution of F and G to be subexponential too, we derive a general asymptotic formula for the finite-time ruin probability. Then, for special cases in which F belongs to the Fréchet or Weibull maximum domain of attraction, we improve this general formula to be transparent.

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On the compound Poisson risk model with dependence based on a generalized Farlie–Gumbel–Morgenstern copula

Cited by 108 publications

References 10 publications

Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula

The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks

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