Optimal periodic strategies with dividends payable from gains only
研究了复合泊松保险风险模型中，仅在周期性决策时点从收益增量中支付股息的最优策略，该策略允许正生存概率，并推导了候选策略下的股息函数。
In this paper, we consider the compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can be paid from the available surplus, then the optimal strategies are often of band or barrier type, resulting in a ruin probability of one (e.g. Albrecher et al. (2011a)). As opposed to such an assumption, we propose that dividends can only be paid from a certain fraction of the gains (i.e. positive increment of the process between successive dividend decision times), and such a constraint allows the surplus process to have a positive survival probability. Some theoretical properties of the value function and the optimal strategy are derived in connection to the Bellman equation. These properties suggest that a bang-bang type of control can be a candidate for the optimal strategy, where dividend is paid at the highest possible amount as long as the surplus is high enough. The dividend function under the candidate strategy is subsequently derived under exponential inter-observation times and claims with a rational Laplace transform, and we also provide specific numerical examples with (mixed) exponential claims where the proposed strategy is optimal in such cases.