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http://hdl.handle.net/10397/89352
| 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) |
| Appears in Collections: | Journal/Magazine Article |
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| a0601-n09_Paper_SICON_final.pdf | Pre-Published version | 514.21 kB | Adobe PDF | View/Open |
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