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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:

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

Software:

Sinc-Pack
PDFBibTeX XMLCite
Full Text: DOI