Analysis of ruin measures for the classical compound Poisson risk model with dependence

Cossette, Hélène; Marceau, Étienne; Marri, Fouad

doi:10.1080/03461230903211992

Cited by 47 publications

(51 citation statements)

References 18 publications

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“…We assume that the interclaim times are distributed according to an Erlang(n) distribution. Therefore our risk model is an extension of the classical compound Poisson risk process proposed by Cossette et al (2010). Therefore our risk model is an extension of the classical compound Poisson risk process proposed by Cossette et al (2010).…”

Section: Introductionmentioning

confidence: 99%

“…The FGM copula is often used in applications to describe dependence structures due to its tractability and simplicity. For more on the FGM copula we refer to Nelsen (2006) and for applications of this in risk theory, health insurance plans, financial risk management, stochastic frontiers and a stereological context see Cossette et al (2010) and the references therein.…”

Section: The Risk Model and The Dependence Structurementioning

confidence: 99%

“…Motivated by Cossette et al (2010), we use the Farlie -Gumbel -Morgenstern (FGM) copula to define the joint distribution of (X, W ) and hence the dependence structure between the claim size and the interclaim time. The FGM copula is defined by…”

Section: The Risk Model and The Dependence Structurementioning

confidence: 99%

“…Therefore our risk model is an extension of the classical compound Poisson risk process proposed by Cossette et al (2010). Therefore our risk model is an extension of the classical compound Poisson risk process proposed by Cossette et al (2010). The choice of an Erlang(n) distribution is motivated by the fact that it is more general than the Exponential distribution allowing a flexible modelling of the interarrival times.…”

Section: Introductionmentioning

confidence: 99%

“…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%

See 4 more Smart Citations

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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Section: Introductionmentioning

confidence: 99%

Section: The Risk Model and The Dependence Structurementioning

confidence: 99%

Section: The Risk Model and The Dependence Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Chadjiconstantinidis

Vrontos

2012

Scandinavian Actuarial Journal

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On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier

Cossette

Marceau

Marri

2012

Appl Stoch Models Bus & Ind

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In this paper, we consider a classical risk process with dependence and in the presence of a constant dividend barrier. The dependence structure between the claim amounts and the interclaim times is introduced through a Farlie–Gumbel–Morgenstern copula. We analyze the expectation of the discounted penalty function and the expectation of the present value of the distributed dividends. For each function, an integro‐differential equation with boundary conditions is derived, and the solution is provided. Finally, we find an explicit solution for each function when the claim amounts are exponentially distributed. We illustrate the impact of the dependence on these two quantities. Copyright © 2012 John Wiley & Sons, Ltd.

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On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

Zhang

Yang

2011

Methodol Comput Appl Probab

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Analysis of ruin measures for the classical compound Poisson risk model with dependence

Cited by 47 publications

References 18 publications

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

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

On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier

On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation

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