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Dividend optimization for regime-switching general diffusions

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  • Zhu, Jinxia
  • Chen, Feng
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    Abstract

    We consider the optimal dividend distribution problem of a financial corporation whose surplus is modeled by a general diffusion process with both the drift and diffusion coefficients depending on the external economic regime as well as the surplus itself through general functions. The aim is to find a dividend payout scheme that maximizes the present value of the total dividends until ruin. We show that, depending on the configuration of the model parameters, there are two exclusive scenarios: (i)the optimal strategy uniquely exists and corresponds to paying out all surpluses in excess of a critical level (barrier) dependent on the economic regime and paying nothing when the surplus is below the critical level;(ii)there are no optimal strategies.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713001066
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 53 (2013)
    Issue (Month): 2 ()
    Pages: 439-456

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    Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:439-456

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Dividend; Dynamic programming principle; General diffusion; Optimization; Regime-switching; IM13; IE20; IB63;

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    References

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    1. Bjarne Højgaard & Michael Taksar, 2001. "Optimal risk control for a large corporation in the presence of returns on investments," Finance and Stochastics, Springer, vol. 5(4), pages 527-547.
    2. Zhu, Jinxia & Yang, Hailiang, 2008. "Ruin theory for a Markov regime-switching model under a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 311-318, February.
    3. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    4. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption-Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279.
    5. Guo, Xin & Liu, Jun & Zhou, Xun Yu, 2004. "A constrained non-linear regular-singular stochastic control problem, with applications," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 167-187, February.
    6. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    7. 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.
    8. 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.
    9. Luis Alvarez & Jukka Virtanen, 2006. "A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation," Economic Theory, Springer, vol. 28(2), pages 373-398, 06.
    10. He, Lin & Liang, Zongxia, 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 88-94, February.
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