Abstract: The optimal dividend paying strategy and optimal asset allocation for insurance companies are studied in this paper. The wealth process is modeled as a portfolio combining a risky asset and a riskless asset as well as a stochastic claim process. The corresponding HJB equation for this problem is derived. Based on a qualitative analysis of the solution, the numerical solution to the equation is obtained. The optimal asset allocation between a risky asset and a riskless asset and the optimal dividend paying strategy are derived.

Key words: HJB equation, numerical solution, optimal asset allocation, optimal dividend paying, portfolio