Numerical Method for a Perturbed Risk Model with Proportional Investment

In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in financial market consisting of risk-free asset risky fixed proportions; assets modeled by jump-diffusion process. Firstly, using theory stochastic process analysis, obtained integro-differential equations satisfied expected discounted payments penalty function. Secondly, numerical approximate solutions through sinc method, since analytical them not easy obtain, found that error is within manageable range. Finally, considered some examples where claim sizes follow an exponential distribution, mixture two distributions or lognormal distribution detail, explored how perturbations investment affect dividends ruin probability. Moreover, sensitive analysis showed proportion investment, diffusion coefficient, claims positive jump all have explicit impacts on