Aggregate Claim Analysis in a Two-sided Exit Setting with Dependence
The two-sided exit problem has been the subject of risk management analysis, used to better understand the dynamic of various insurance risk processes. In the two-sided exit setting, the discounted aggregate claims are investigated under a dependent renewal process (also known as dependent Sparre Andersen risk process). Utilizing Lundberg's generalized equation and Laplace transform, we identify the fundamental solutions to a given integral equation, which will be shown to play a role similar to the scale matrix for spectrally-negative Markov-additive processes. Explicit expressions and recursions are then identified for the two-sided probabilities and the moments of the aggregate claims respectively. A numerical example for the two-sided exit probabilities involving the Farlie-Gumbel-Morgenstern (FGM) copula is provided.
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Tuesday, June 13, 2017 - 14:30 to 15:00
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