Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment

In this paper, we consider a risk model with two-sided jumps and proportional investment. The upward downward represent gains claims, respectively. Suppose the company invests all of its surplus in certain proportion two types investments, one is risk-free (such as bank accounts) other risky stocks). Our aim to find optimal admissible strategy (including dividend rate ratio investment assets), maximize value function, discuss effects number parameters on payments. Firstly, HJB equation function obtained by stochastic analysis theory dynamic programming method, obtained. Since integro-differential satisfied difficult solve, turn sinc numerical method approximate solve it. Then, error between exact solution (ES) (SA) analyzed. Finally, relative special an ES given, some examples sensitivity are discussed. This study provides theoretical basis for insurance companies prevent risks better.