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Optimal dividends under Markov-modulated bankruptcy level

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  • Ferrari, Giorgio
  • Schuhmann, Patrick
  • Zhu, Shihao

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.

Suggested Citation

  • Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2022. "Optimal dividends under Markov-modulated bankruptcy level," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 146-172.
    • Handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:146-172
    DOI: 10.1016/j.insmatheco.2022.06.005
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    References listed on IDEAS

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    21. Jiang, Zhengjun, 2019. "Optimal dividend policy when risk reserves follow a jump–diffusion process with a completely monotone jump density under Markov-regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 1-7.
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    Cited by:

    1. Aïd, René & Basei, Matteo & Ferrari, Giorgio, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Center for Mathematical Economics Working Papers 679, Center for Mathematical Economics, Bielefeld University.
    2. Ren'e Aid & Matteo Basei & Giorgio Ferrari, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Papers 2305.00541, arXiv.org.

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    More about this item

    Keywords

    Optimal dividend policy; Regime-switching; Regime-dependent bankruptcy levels; HJB equation; Singular stochastic control;
    All these keywords.

    JEL classification:

    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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