PORTFOLIO OPTIMIZATION IN AFFINE MODELS WITH MARKOV SWITCHING

Marcos Escobar Anel (), Daniela Neykova () and Rudi Zagst ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 05, 1-46

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.

Keywords: Utility maximization; HJB equations; affine models; Markov switching (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Working Paper: Portfolio Optimization in Affine Models with Markov Switching (2014)
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DOI: 10.1142/S0219024915500302

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