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. 125158. ISSN 03461238

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Abstract
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 FarlieGumbelMorgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the interarrival 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 GerberShiu 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:  Integrodifferential equation; ruin probability; dependence; defective renewal equation; GerberShiu discounted penalty function; Laplace Transform; FarlieGumbelMorgenstern 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 
URI:  http://repository.essex.ac.uk/id/eprint/11546 
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