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Analysis of ruin measures for the classical compound Poisson risk model with dependence. (English) Zbl 1226.91024

Summary: We consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie-Gumbel-Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber-Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.

MSC:

91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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