Optimal dividend policy when risk reserves follow a jump-diffusion process with a completely monotone jump density under Markov-regime switching

The paper studies optimal dividend distribution for an insurance company whose risk reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with a completely monotone jump density where jump densities and parameters including discount rate are modulated by a finite-state irreducible Markov chain. The major goal is to maximize the expected cumulative discounted dividend payments until ruin time when risk reserve is less than or equal to zero for the first time. I extend the results of Jiang (2015) for a Markov-modulated jump-diffusion process from exponential jump densities to completely monotone jump densities by proving that it is also optimal to take a modulated barrier strategy at some positive regime-dependent levels and that value function as the fixed point of a contraction is explicitly characterized. (C) 2019 Elsevier B.V. All rights reserved.