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Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility

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  • Holger Kraft

Abstract

Given an investor maximizing utility from terminal wealth with respect to a power utility function, we present a verification result for portfolio problems with stochastic volatility. Applying this result, we solve the portfolio problem for Heston's stochastic volatility model. We find that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium. Finally, it is demonstrated that the results critically hinge upon the specification of the market price of risk. We conclude that, in applications, one has to be very careful when exogenously specifying the form of the market price of risk.

Suggested Citation

  • Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:3:p:303-313
    DOI: 10.1080/14697680500149503
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    References listed on IDEAS

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    1. Liu, Jun, 2001. "Dynamic Choice and Risk Aversion," University of California at Los Angeles, Anderson Graduate School of Management qt36v1d9zg, Anderson Graduate School of Management, UCLA.
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