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Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching


  • Luz Rocío Sotomayor
  • Abel Cadenillas


We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite‐state continuous‐time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a “bull market” than in a “bear market.” This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk‐averse investors will consume relatively more in a “bull market” than in a “bear market,” and the opposite is true for low risk‐averse investors.

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  • 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.
  • Handle: RePEc:bla:mathfi:v:19:y:2009:i:2:p:251-279
    DOI: 10.1111/j.1467-9965.2009.00366.x

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    References listed on IDEAS

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    1. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697,, revised Sep 2018.
    2. Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    3. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    4. Hu, Fengxia & Wang, Rongming, 2017. "Optimal investment–consumption strategy with liability and regime switching model under Value-at-Risk constraint," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 103-118.
    5. Zhu, Jinxia & Chen, Feng, 2013. "Dividend optimization for regime-switching general diffusions," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 439-456.
    6. Yehong Yang & Guohua Cao, 2019. "Optimal Financing and Dividend Strategies with Time Inconsistency in a Regime Switching Economy," Complexity, Hindawi, vol. 2019, pages 1-11, April.
    7. Paul Gassiat & Fausto Gozzi & Huy^en Pham, 2011. "Investment/consumption problem in illiquid markets with regime-switching," Papers 1107.4210,, revised Apr 2012.
    8. Jianmin Shi, 2020. "Optimal control of multiple Markov switching stochastic system with application to portfolio decision," Papers 2010.16102,
    9. Chen, Zhiping & Li, Gang & Zhao, Yonggan, 2014. "Time-consistent investment policies in Markovian markets: A case of mean–variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 293-316.
    10. Zou, Bin & Cadenillas, Abel, 2014. "Explicit solutions of optimal consumption, investment and insurance problems with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 159-167.
    11. Vladimir Dombrovskii & Tatyana Obyedko, 2014. "Dynamic Investment Portfolio Optimization under Constraints in the Financial Market with Regime Switching using Model Predictive Control," Papers 1410.1136,
    12. Ni, Zhong-Xin & Wang, Da-Zhong & Xue, Wen-Jun, 2015. "Investor sentiment and its nonlinear effect on stock returns—New evidence from the Chinese stock market based on panel quantile regression model," Economic Modelling, Elsevier, vol. 50(C), pages 266-274.
    13. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    14. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    15. Marcos Escobar & Daniela Neykova & Rudi Zagst, 2015. "Portfolio Optimization In Affine Models With Markov Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-46.
    16. Michael Ludkovski & Hyekyung Min, 2010. "Illiquidity Effects in Optimal Consumption-Investment Problems," Papers 1004.1489,, revised Sep 2010.
    17. Bin Zou & Abel Cadenillas, 2014. "Optimal Investment and Risk Control Problem for an Insurer: Expected Utility Maximization," Papers 1402.3560,, revised Mar 2014.
    18. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    19. 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.
    20. Zhang, Miao & Chen, Ping & Yao, Haixiang, 2017. "Mean-variance portfolio selection with only risky assets under regime switching," Economic Modelling, Elsevier, vol. 62(C), pages 35-42.
    21. Zeng, Yan & Wu, Huiling & Lai, Yongzeng, 2013. "Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon," Economic Modelling, Elsevier, vol. 33(C), pages 462-470.
    22. Suhan Altay & Katia Colaneri & Zehra Eksi, 2019. "Optimal Convergence Trading with Unobservable Pricing Errors," Papers 1910.01438,, revised Oct 2019.
    23. Bin Zou & Abel Cadenillas, 2014. "Explicit Solutions of Optimal Consumption, Investment and Insurance Problem with Regime Switching," Papers 1402.3562,, revised Jun 2014.
    24. Bin Zou & Abel Cadenillas, 2017. "Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-22, January.
    25. Sühan Altay & Katia Colaneri & Zehra Eksi, 0. "Optimal convergence trading with unobservable pricing errors," Annals of Operations Research, Springer, vol. 0, pages 1-29.

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