A stochastic volatility model and optimal portfolio selection

Abstract

In this paper, first we study a stochastic volatility market model for which an explicit candidate solution to the problem of maximizing the utility function of terminal wealth is obtained. Applying this result, we present a complete solution for the Heston model, which is a particular case of the general model. A verification result and a martingale representation of the solution are provided for the Heston model. Finally, the same techniques are used to study a stochastic interest rate model and a necessary and sufficient condition for exploding growth is presented.

Keywords:

• Optimal portfolio
• HJB equation
• Stochastic volatility
• Heston model
• Square-root process

JEL Classification:

• C
• C6
• C61
• D
• D8
• D81
• G
• G1
• G11

Acknowledgements

We are very grateful to the Editors and an anonymous referee for their insightful and detailed comments that substantially improved the paper. We thank H. Kraft for kindly sending us the latest version of his article.