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Optimal financing and dividend distribution in a general diffusion model with regime switching

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  • Jinxia Zhu
  • Hailiang Yang

Abstract

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injections and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of capital injections. We prove that it is optimal to inject capitals only when the surplus tends to fall below zero and to pay out dividends at the maximal rate when the surplus is at or above the threshold dependent on the environment regime.

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  • Jinxia Zhu & Hailiang Yang, 2015. "Optimal financing and dividend distribution in a general diffusion model with regime switching," Papers 1506.08360, arXiv.org.
    • Handle: RePEc:arx:papers:1506.08360
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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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    5. 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.
    6. Zhu, Jinxia, 2014. "Dividend Optimization For A Regime-Switching Diffusion Model With Restricted Dividend Rates," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 459-494, May.
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    11. 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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