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Optimal investment in multidimensional Markov-modulated affine models

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  • Daniela Neykova
  • Marcos Escobar
  • Rudi Zagst

Abstract

In a multidimensional affine framework we consider a portfolio optimization problem with finite horizon, where an investor aims to maximize the expected utility of her terminal wealth. We state a very flexible asset price model that incorporates several risk factors modeled both by diffusion processes and by a Markov chain. Exploiting the affine structure of the model we solve the corresponding Hamilton–Jacobi–Bellman equations explicitly up to an expectation only over the Markov chain or equivalently up to a system of simple ODEs. The relevance of the presented model is illustrated on two examples including a stochastic short rate model with trading in the bond and the stock market, and a multidimensional stochastic volatility and stochastic correlation model. Precise verification results for both examples are provided. Economic interpretations of the models and results complement the theoretical analysis. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:kap:annfin:v:11:y:2015:i:3:p:503-530
    DOI: 10.1007/s10436-015-0268-y
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    Cited by:

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    More about this item

    Keywords

    HJB systems; Utility maximization; Multidimensional affine models; Markov chains; G11; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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