Numerical Solution for the Dividend Value Function of a Dual Risk Model With Investment

This paper proposes a dual risk model with liquid reserve and proportional investments, this model is more suitable for real life. We derive the integral differential equations for the expected total discounted dividends before ruin. Since the exact solution of the equations does not exist, we obtain the approximate solution expression and further deduce the upper limit of the error caused by the approximate method for some special cases. In particular, we analyze the effect of the correlation volume on the expected total discounted dividend through two examples. Then, we also provide a special case to test the superiority of the sinc method, the results show that the sinc method is superior in solving approximate solutions. This study can help companies avoid potential liquidity risks, financial risks, and ensure the robust operation of the company.