2019/01/10 by Kei Noba, José Luis Pérez, Noba, Kei +3
Decision Sciences · Health Professions · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Global Health Care Issues #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1901.03021
openalex publication_date 2019/01/10 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
This paper studies the bail-out optimal dividend problem with regime\nswitching under the constraint that the cumulative dividend strategy is\nabsolutely continuous. We confirm the optimality of the regime-modulated\nrefraction-reflection strategy when the underlying risk model follows a general\nspectrally negative Markov additive process. To verify the conjecture of a\nbarrier type optimal control, we first introduce and study an auxiliary problem\nwith the final payoff at an exponential terminal time and characterize the\noptimal threshold explicitly using fluctuation identities of the\nrefracted-reflected Levy process. Second, we transform the problem with\nregime-switching into an equivalent local optimization problem with a final\npayoff up to the first regime switching time. The refraction-reflection\nstrategy with regime-modulated thresholds can be shown as optimal by using\nresults in the first step and some fixed point arguments for auxiliary\nrecursive iterations.\n