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Portfolio Optimization In Affine Models With Markov Switching

Author

Listed:
  • MARCOS ESCOBAR

    (Department of Mathematics, Ryerson University, 350 Victoria St., Toronto ON M5B 2K3, Canada)

  • DANIELA NEYKOVA

    (Chair of Mathematical Finance, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany)

  • RUDI ZAGST

    (Chair of Mathematical Finance, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany)

Abstract

We consider a stochastic-factor financial model wherein the asset price and the stochastic-factor processes depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this end we apply Merton's approach, because we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains, we first derive the Hamilton–Jacobi–Bellman (HJB) equations that, in our case, correspond to a system of coupled nonlinear partial differential equations (PDE). 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 that leads to explicit solutions. General verification results are also proved. The results are illustrated for the special case of a Markov-modulated Heston model.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:05:n:s0219024915500302
    DOI: 10.1142/S0219024915500302
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    2. Suhan Altay & Katia Colaneri & Zehra Eksi, 2019. "Optimal Convergence Trading with Unobservable Pricing Errors," Papers 1910.01438, arXiv.org, revised Oct 2019.
    3. 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.
    4. 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.
    5. 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.
    6. Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for L{\'e}vy switching models," Papers 1807.08982, arXiv.org.
    7. 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.
    8. Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for Lévy switching models," Working Papers hal-01844635, HAL.

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