The maximum surplus before ruin for dependent risk models through Farlie–Gumbel–Morgenstern copula. Issue 5 (27th May 2016)

• Record Type: Journal Article
• Authors: Jiang, Wuyuan; Yang, Zhaojun
• Is Part Of: Scandinavian actuarial journal. Volume 2016:Issue 5(2016)
• Page Start: 385
• Page End: 397
• Publication Date: 2016-05-27
• Subjects: dependent risk model -- distribution of the maximum surplus -- Farlie–Gumbel–Morgenstern copula -- integro-differential equation -- explicit distribution; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2014.936972
• Languages: English
• ISSNs: 0346-1238

Abstract

Abstract : We extend the classical compound Poisson risk model to consider the distribution of the maximum surplus before ruin where the claim sizes depend on inter-claim times via the Farlie–Gumbel–Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for this distribution, of which the Laplace transform is provided. We obtain the renewal equation and explicit expressions for this distribution are derived when the claim amounts are exponentially distributed. Finally, we present numerical examples.