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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.

MSC:
91B30Risk theory, insurance
91G60Numerical methods in mathematical finance
35Q91PDEs in connection with game theory, economics, social and behavioral sciences
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Sinc-Pack
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