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Title: On the bailout dividend problem for spectrally negative markov additive models
Authors: Noba, K
Pérez, JL
Yu, X 
Issue Date: 2020
Source: SIAM journal on control and optimization, 2020, v. 58, no. 2, p. 1049-1076
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.
Keywords: Absolutely continuous constraint
Capital injection
Fixed point argument
Refracted-reflected spectrally negative Lévy process
Regime switching
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on control and optimization 
ISSN: 0363-0129
EISSN: 1095-7138
DOI: 10.1137/19M1298172
Rights: © 2020, Society for Industrial and Applied Mathematics.
Unauthorized reproduction of this article is prohibited.
First Published in SIAM Journal on Control and Optimization in Volume 58, Issue 2, published by the Society for Industrial and Applied Mathematics (SIAM)
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