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Classical and singular stochastic control for the optimal dividend policy when there is regime switching

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  • Sotomayor, Luz R.
  • Cadenillas, Abel

Abstract

Motivated by economic and empirical arguments, we consider a company whose cash surplus is affected by macroeconomic conditions. Specifically, we model the cash surplus as a Brownian motion with drift and volatility modulated by an observable continuous-time Markov chain that represents the regime of the economy. The objective of the management is to select the dividend policy that maximizes the expected total discounted dividend payments to be received by the shareholders. We study two different cases: bounded dividend rates and unbounded dividend rates. These cases generate, respectively, problems of classical stochastic control with regime switching and singular stochastic control with regime switching. We solve these problems, and obtain the first analytical solutions for the optimal dividend policy in the presence of business cycles. We prove that the optimal dividend policy depends strongly on macroeconomic conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:3:p:344-354
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    References listed on IDEAS

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    1. 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, January.
    2. 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.
    3. Asmussen, Søren & Frey, Andreas & Rolski, Tomasz & Schmidt, Volker, 1995. "Does Markov-Modulation Increase the Risk?," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 49-66, May.
    4. Bauerle, Nicole, 1996. "Some results about the expected ruin time in Markov-modulated risk models," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 119-127, July.
    5. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    6. T. Choulli & M. Taksar & X. Y. Zhou, 2001. "Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 573-596.
    7. Radner, Roy & Shepp, Larry, 1996. "Risk vs. profit potential: A model for corporate strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1373-1393, August.
    8. 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.
    9. Guo, Xin & Miao, Jianjun & Morellec, Erwan, 2005. "Irreversible investment with regime shifts," Journal of Economic Theory, Elsevier, vol. 122(1), pages 37-59, May.
    10. Lu, Yi & Li, Shuanming, 2009. "The Markovian regime-switching risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 296-303, April.
    11. 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, April.
    12. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    13. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    14. 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.
    15. Michael I. Taksar, 2000. "Optimal risk and dividend distribution control models for an insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 1-42, February.
    16. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    17. Reinhard, Jean-Marie, 1984. "On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 23-43, April.
    18. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    19. 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.
    20. Taksar, Michael I. & Zhou, Xun Yu, 1998. "Optimal risk and dividend control for a company with a debt liability," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 105-122, May.
    21. Bong‐Gyu Jang & Hyeng Keun Koo & Hong Liu & Mark Loewenstein, 2007. "Liquidity Premia and Transaction Costs," Journal of Finance, American Finance Association, vol. 62(5), pages 2329-2366, October.
    22. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    23. 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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