A compound Poisson risk model with proportional investment. (English) Zbl 1282.91147

Summary: We consider the compound Poisson risk model with a threshold dividend strategy and proportional investment. The goal here is to investigate the expected discounted dividend payments and the expected penalty-reward function. Integro-differential equations with certain boundary conditions are derived. As closed-form solutions do not exist, a numerical sinc method is proposed. Finally, some examples illustrating the procedure are presented.


91B30 Risk theory, insurance (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences


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