Dividend Maximization under Consideration of the Time Value of Ruin∗

In the Cramér-Lundberg model and its di usion approximation, it is a classical problem to nd the optimal dividend payment strategy that maximizes the expected value of the discounted dividend payments until ruin. One often raised disadvantage of this approach is the fact that such a strategy does not take the life time of the controlled process into account. In this paper we introduce a value function which considers both expected dividends and the time value of ruin. For both the di usion model and the Cramér-Lundberg model with exponential claim sizes, the problem is solved and in either case the optimal strategy is identi ed, which for unbounded dividend intensity is a barrier strategy and for bounded dividend intensity is of threshold type.