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Optimal Dividends under Markov-Modulated Bankruptcy Level

Giorgio Ferrari, Patrick Schuhmann and Shihao Zhu
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Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Patrick Schuhmann: Center for Mathematical Economics, Bielefeld University
Shihao Zhu: Center for Mathematical Economics, Bielefeld University

No 657, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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.

Keywords: Optimal dividend policy; Regime-switching; Regime-dependent bankruptcy levels; HJB equation; Singular stochastic control (search for similar items in EconPapers)
Pages: 35
Date: 2021-11-15
New Economics Papers: this item is included in nep-cfn and nep-cwa
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https://pub.uni-bielefeld.de/download/2959047/2959048 First Version, 2021 (application/pdf)

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