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Abstract

This paper proposes and solves 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 simul-

taneously: 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, is 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 theoret-

ical 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.

Abstract

MSC Classification: 91B70, 93E20, 60H30