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Optimal dividend policy when risk reserves follow a jump–diffusion process with a completely monotone jump density under Markov-regime switching

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  • Jiang, Zhengjun

Abstract

The paper studies optimal dividend distribution for an insurance company whose risk reserves in the absence of dividends follow a Markov-modulated jump–diffusion process with a completely monotone jump density where jump densities and parameters including discount rate are modulated by a finite-state irreducible Markov chain. The major goal is to maximize the expected cumulative discounted dividend payments until ruin time when risk reserve is less than or equal to zero for the first time. I extend the results of Jiang (2015) for a Markov-modulated jump–diffusion process from exponential jump densities to completely monotone jump densities by proving that it is also optimal to take a modulated barrier strategy at some positive regime-dependent levels and that value function as the fixed point of a contraction is explicitly characterized.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:1-7
    DOI: 10.1016/j.insmatheco.2019.01.011
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    References listed on IDEAS

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    1. Abel Cadenillas & Sudipto Sarkar & Fernando Zapatero, 2007. "Optimal Dividend Policy With Mean‐Reverting Cash Reservoir," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 81-109, January.
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    6. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    7. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    8. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    9. Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
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    11. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    12. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
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    Cited by:

    1. 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.
    2. Chongrui Zhu, 2021. "Optimality of threshold strategies for spectrally negative Levy processes and a positive terminal value at creeping ruin," Papers 2107.06841, arXiv.org, revised Jan 2023.

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    More about this item

    Keywords

    Optimal dividend policy; Markov-modulated jump–diffusion process; Completely monotone jump density; q-scale functions; Fixed point theorem;
    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

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