On the bail-out dividend problem for spectrally negative Markov additive models

Kei Noba, José Luis Pérez, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1049-1076
Number of pages28
JournalSIAM Journal on Control and Optimization
Volume58
Issue number2
DOIs
Publication statusPublished - 8 Apr 2020

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