Optimal dividend payments in classical risk model with capital injections and solvency constraints

This paper deals with the optimal control problem for the classical risk model with solvency constraints. The objective of the corporation is to maximize the cumulative expected discounted dividends payout minus the equity issuance with solvency constraints. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b* so that whenever surplus goes above b*, the excess is paid out as dividends. However, the optimal level b* may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level b
0
> b*. We show that in this case a barrier strategy at b
0
is optimal.