On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums
研究了保险公司在保费依赖盈余时的最优分红策略，目标是最大化破产前累计折现分红与破产时惩罚之和，给出了单分红带策略最优的充要条件。
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The objective consists in maximizing the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated Hamilton–Jacobi–Bellman equation and find necessary and sufficient conditions for optimality of a single dividend-band strategy, in terms of particular Gerber–Shiu functions. A number of concrete examples are analyzed.