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Dividend optimization for regime-switching general diffusions

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  • Zhu, Jinxia
  • Chen, Feng

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.

Suggested Citation

  • Zhu, Jinxia & Chen, Feng, 2013. "Dividend optimization for regime-switching general diffusions," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 439-456.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:439-456
    DOI: 10.1016/j.insmatheco.2013.07.006
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    References listed on IDEAS

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    1. 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.
    2. Abel Cadenillas & Tahir Choulli & Michael Taksar & Lei Zhang, 2006. "Classical And Impulse Stochastic Control For The Optimization Of The Dividend And Risk Policies Of An Insurance Firm," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 181-202.
    3. Luis Alvarez & Jukka Virtanen, 2006. "A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 373-398, June.
    4. 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.
    5. repec:sbe:breart:v:24:y:2004:i:2:a:2711 is not listed on IDEAS
    6. Nicole Bäuerle, 2004. "Approximation of Optimal Reinsurance and Dividend Payout Policies," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 99-113.
    7. repec:spr:compst:v:51:y:2000:i:1:p:1-42 is not listed on IDEAS
    8. 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.
    9. 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.
    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.
    11. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    12. 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.
    13. 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.
    14. 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.
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    Citations

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    Cited by:

    1. Igor G. Pospelov & Stanislav A. Radionov, 2015. "Optimal Dividend Policy When Cash Surplus Follows The Telegraph Process," HSE Working papers WP BRP 48/FE/2015, National Research University Higher School of Economics.
    2. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
    3. Jinxia Zhu & Hailiang Yang, 2015. "Optimal financing and dividend distribution in a general diffusion model with regime switching," Papers 1506.08360, arXiv.org.

    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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