On the bailout dividend problem with periodic dividend payments for spectrally negative Markov additive processes

This paper studies the bailout optimal dividend problem with regime switching under constraint that payments can be made only at arrival times of an independent Poisson process while capital injected continuously in time. We show optimality regime-modulated Parisian-classical reflection strategy when underlying risk model follows a general spectrally negative Markov additive process. In order to verify optimality, first we study auxiliary driven by single Lévy final payoff exponential terminal time and characterize strategy. Then, use dynamic programming principle transform global regime-switching into equivalent local optimization up The modulated barrier proven using results from approximations via recursive iterations.