A stochastic volatility model and optimal portfolio selection

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.