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Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisions

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  • Weiyin Fei

Abstract

This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using the generalized HJB equation, we deduce the optimal consumption and portfolio policies under uncertain stochastic financial markets with Markovian switching. Finally, for constant relative risk-aversion (CRRA) felicity functions, we explicitly obtain the optimal consumption and portfolio policies. Moreover, we also make an economic analysis through numerical examples.

Suggested Citation

  • Weiyin Fei, 2014. "Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisions," Papers 1401.2531, arXiv.org.
    • Handle: RePEc:arx:papers:1401.2531
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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    3. Q. Zhang & G. Yin, 2004. "Nearly-Optimal Asset Allocation in Hybrid Stock Investment Models," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 419-444, May.
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    5. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    6. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

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    2. 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.
    3. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    4. Yaacov Kopeliovich & Michael Pokojovy & Julia Bernatska, 2024. "On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility," Papers 2403.15923, arXiv.org, revised Nov 2024.
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    6. Jianmin Shi, 2023. "Dynamic asset allocation with multiple regime‐switching markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(2), pages 1741-1755, April.

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