On the Bailout Dividend Problem for Spectrally Negative Markov Additive Models
On the Bailout Dividend Problem for Spectrally Negative Markov Additive Models
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DOI：
10.1137/19m1298172
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Kei Noba;José-Luis Pérez;Xiang Yu
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文献类型：
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作者：
Kei Noba;José-Luis Pérez;Xiang Yu
本文研究了在累积股息策略绝对连续的约束下，存在制度转换的救助最优股息问题。我们确认的政权调制折射反射策略的最优性时，基本的风险模型遵循一般谱负马尔可夫加性过程。为了验证屏障型最优控制的猜想，我们首先引入并研究了一个最终收益在指数终端时间的辅助问题，并利用折射-反射Levy过程的波动恒等式明确地刻画了最优阈值.第二，我们把问题与政权切换到一个等价的局部优化问题的最终回报的第一政权切换时间。通过使用第一步的结果和辅助递归迭代的一些不动点参数，可以证明具有状态调制阈值的折射-反射策略是最优的。
This paper studies the bail-out 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 Levy 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.