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 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 verication result and a martingale representation of the solution are providedfor 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