Optimal investment with transaction costs and dividends for an insurer

This paper investigates the optimal investment problems for an insurer whose reserve process is approximated by a diffusion model. The insurer is allowed to invest its wealth in the financial market consisting of one risk-free asset (bond) and one risky asset (stock). There are charges which equal to a fixed percentage of the amount transferred between the two assets. Under different criteria, we consider two optimization problems: one is maximizing the expected discounted utility of the dividends; the other is maximizing the insurer's expected utility of the terminal wealth. We obtain that the optimal investment strategies are bang-bang strategies in both of the two problems. Numerical examples are given to illustrate our results.