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Portfolio Optimization in Affine Models with Markov Switching

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  • Marcos Escobar
  • Daniela Neykova
  • Rudi Zagst

Abstract

We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this aim we apply Merton's approach, as we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains we first derive the HJB equations, which in our case correspond to a system of coupled non-linear PDEs. Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage we propose a separable ansatz, which leads to explicit solutions in this case as well. General verification results are also proved. The results are illustrated for the special case of a Markov modulated Heston model.

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  • Marcos Escobar & Daniela Neykova & Rudi Zagst, 2014. "Portfolio Optimization in Affine Models with Markov Switching," Papers 1403.5247, arXiv.org.
    • Handle: RePEc:arx:papers:1403.5247
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    Cited by:

    1. Daniela Neykova & Marcos Escobar & Rudi Zagst, 2015. "Optimal investment in multidimensional Markov-modulated affine models," Annals of Finance, Springer, vol. 11(3), pages 503-530, November.
    2. Sühan Altay & Katia Colaneri & Zehra Eksi, 2021. "Optimal convergence trading with unobservable pricing errors," Annals of Operations Research, Springer, vol. 299(1), pages 133-161, April.
    3. Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for Lévy switching models," Working Papers hal-01844635, HAL.
    4. Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for L{\'e}vy switching models," Papers 1807.08982, arXiv.org.
    5. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    6. Christoph Belak & Sören Christensen & Olaf Menkens, 2016. "Worst-Case Portfolio Optimization In A Market With Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-36, March.
    7. Suhan Altay & Katia Colaneri & Zehra Eksi, 2019. "Optimal Convergence Trading with Unobservable Pricing Errors," Papers 1910.01438, arXiv.org, revised Oct 2019.
    8. 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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