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

Chadjiconstantinidis, Stathis and Vrontos, Spyridon (2014) 'On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula.' Scandinavian Actuarial Journal, 2014 (2). pp. 125-158. ISSN 0346-1238

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In this article, 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-Gumbel-Morgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalised Lundberg equation, the Laplace transform (LT) 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 LT 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 LT of the time to ruin are given. © 2014 Copyright Taylor & Francis Group, LLC.

Item Type: Article
Uncontrolled Keywords: Integro-differential equation; ruin probability; dependence; defective renewal equation; Gerber-Shiu discounted penalty function; Laplace Transform; Farlie-Gumbel-Morgenstern copula
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Jul 2013 15:06
Last Modified: 15 Jan 2022 00:47

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