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The compound Poisson risk model with a threshold strategy under constant interest. (Chinese. English summary) Zbl 1265.91164

Summary: In this paper, we consider the expected discounted penalty function for a compound Poisson risk process with a threshold strategy under constant interest. Firstly, the integro-differential equations and their explicit solutions are derived. Secondly, expressions for the ruin probability and the joint distribution of the surplus immediately before ruin and the deficit at ruin are given. Finally, it is obtained that the integro-differential equations are satisfied by the expected discounted penalty function when the risk process is perturbed by diffusion.

MSC:

91G80 Financial applications of other theories
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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