论文标题
在频谱正面马尔可夫添加剂模型下的最佳股息和资本注入
Optimal dividend and capital injection under spectrally positive Markov additive models
论文作者
论文摘要
本文研究了Finetti在马尔可夫添加剂模型下对资本注入的最佳股息问题。基于动态编程原则，我们首先研究了一个辅助奇异控制问题，并在指数随机时间的最终回报。双重屏障策略被证明是最佳的，最佳屏障使用频谱正征费过程的波动身份以分析形式表征。然后，我们将原始问题在频谱积极的马尔可夫添加剂模型下转换为等效系列的本地优化问题，并在制度转换时间的最终收益中。可以使用辅助问题的结果和递归迭代的固定点论证来确认制度调制的双重屏障策略的最佳性。
This paper studies De Finetti's optimal dividend problem with capital injection under spectrally positive Markov additive models. Based on dynamic programming principle, we first study an auxiliary singular control problem with a final payoff at an exponential random time. The double barrier strategy is shown to be optimal and the optimal barriers are characterized in analytical form using fluctuation identities of spectrally positive Levy processes. We then transform the original problem under spectrally positive Markov additive models into an equivalent series of local optimization problems with the final payoff at the regime-switching time. The optimality of the regime-modulated double barrier strategy can be confirmed for the original problem using results from the auxiliary problem and the fixed point argument for recursive iterations.
