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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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    Citations

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    Cited by:

    1. Ferrari, Giorgio & Yang, Shuzhen, 2016. "On an optimal extraction problem with regime switching," Center for Mathematical Economics Working Papers 562, Center for Mathematical Economics, Bielefeld University.
    2. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    3. 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.
    4. D’Auria, Bernardo & Kella, Offer, 2012. "Markov modulation of a two-sided reflected Brownian motion with application to fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1566-1581.
    5. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
    6. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    7. Xiaoxiao Zheng & Xin Zhang, 2014. "Optimal Hybrid Dividend Strategy Under The Markovian Regime-Switching Economy," Papers 1406.7606, arXiv.org.
    8. Zhu, Jinxia & Chen, Feng, 2013. "Dividend optimization for regime-switching general diffusions," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 439-456.
    9. Giorgio Ferrari & Shuzhen Yang, 2016. "On an Optimal Extraction Problem with Regime Switching," Papers 1602.06765, arXiv.org, revised Dec 2017.
    10. Chen, Shumin & Li, Zhongfei & Zeng, Yan, 2014. "Optimal dividend strategies with time-inconsistent preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 150-172.
    11. Jinxia Zhu & Hailiang Yang, 2015. "Optimal financing and dividend distribution in a general diffusion model with regime switching," Papers 1506.08360, arXiv.org.

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