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The maximum surplus before ruin for dependent risk models through Farlie-Gumbel-Morgenstern copula. (English) Zbl 1401.91149

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
62E15 Exact distribution theory in statistics
62P05 Applications of statistics to actuarial sciences and financial mathematics
60K05 Renewal theory
45J05 Integro-ordinary differential equations
44A10 Laplace transform
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