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

TL;DR

This paper investigates an optimal dividend payout strategy for spectrally negative Markov additive processes with regime switching, showing that a regime-modulated Parisian-classical reflection strategy is optimal under specific constraints.

Contribution

It introduces and proves the optimality of a regime-modulated Parisian-classical reflection strategy for dividend payments in a regime-switching spectrally negative Markov additive process.

Findings

Optimality of regime-modulated Parisian-classical reflection strategy.

Reduction of the global problem to a local optimization problem.

Verification of strategy optimality using auxiliary problems and recursive approximations.

Abstract

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