Optimal Dividends under Markov-Modulated Bankruptcy Level

TL;DR

This paper analyzes an optimal dividend payout problem in a regime-switching environment affecting cash surplus and bankruptcy levels, providing explicit solutions and numerical insights into optimal strategies.

Contribution

It introduces a novel model where bankruptcy levels are regime-dependent and derives explicit optimal dividend policies with detailed sensitivity analysis.

Findings

Optimal strategies can be barrier-type or liquidation-barrier type.

Explicit formulas for value functions and policies are obtained.

Numerical analysis reveals parameter sensitivities of the optimal policy.

Abstract

This paper proposes and studies an optimal dividend problem in which a two-state regime-switching environment affects the dynamics of the company's cash surplus and, as a novel feature, also the bankruptcy level. The aim is to maximize the total expected profits from dividends until bankruptcy. The company's optimal dividend payout is therefore influenced by four factors simultaneously: Brownian fluctuations in the cash surplus, as well as regime changes in drift, volatility and bankruptcy levels. In particular, the average profitability can assume different signs in the two regimes. We find a rich structure of the optimal strategy, which, depending on the interaction of the model's parameters, can be either of barrier-type or of liquidation-barrier type. Furthermore, we provide explicit expressions of the optimal policies and value functions. Finally, we complement our theoretical results by a detailed numerical study, where also a thorough analysis of the sensitivities of the optimal dividend policy with respect to the problem's parameters is performed.