Optimal dividends under Markov-modulated bankruptcy level

Giorgio Ferrari, Patrick Schuhmann and Shihao Zhu

Insurance: Mathematics and Economics, 2022, vol. 106, issue C, 146-172

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.

Keywords: Optimal dividend policy; Regime-switching; Regime-dependent bankruptcy levels; HJB equation; Singular stochastic control (search for similar items in EconPapers)
JEL-codes: C61 E32 G35 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:106:y:2022:i:c:p:146-172

DOI: 10.1016/j.insmatheco.2022.06.005

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