Chen, Xu; Ou, Hui A compound Poisson risk model with proportional investment. (English) Zbl 1282.91147 J. Comput. Appl. Math. 242, 248-260 (2013). 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. Cited in 5 Documents 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 Keywords:discounted dividend payments; Gerber-Shiu discounted penalty function; integro-differential equation; sinc numerical methods Software:Sinc-Pack PDFBibTeX XMLCite \textit{X. Chen} and \textit{H. Ou}, J. Comput. Appl. Math. 242, 248--260 (2013; Zbl 1282.91147) Full Text: DOI