SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 1049-1076, January 2020.
This paper studies the bailout optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection strategy when the underlying risk model follows a general spectrally negative Markov additive process. To verify the conjecture of a barrier-type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected Lévy process. Second, we transform the problem with regime switching into an equivalent local optimization problem with a final payoff up to the first regime-switching time. The refraction-reflection strategy with regime-modulated thresholds can be shown as optimal by using results in the first step and some fixed point arguments for auxiliary recursive iterations.

中文翻译：

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谱负马尔可夫加性模型的救助股利问题

SIAM控制与优化杂志，第58卷，第2期，第1049-1076页，2020年1月。
本文在累积红利策略绝对连续的约束条件下，研究了制度转换下的救助最优红利问题。当基础风险模型遵循一般的光谱负马尔可夫加法过程时，我们确认了制度调制折射反射策略的最优性。为了验证障碍型最优控制的猜想，我们首先介绍和研究一个在指数终极时间具有最终收益的辅助问题，并使用折射反射Lévy过程的波动恒等式明确描述最优阈值。其次，我们将政权转换问题转化为等效的局部优化问题，其最终收益可达到第一个政权转换时间。