Asset valuation with unhedgeable risks

We study a model of optimal portfolio choice for a single agent where investments take place between a bond and a stock account. The price of the bond is riskless as opposed to the price of the stock which is a diffusion process. The coefficients of the latter depend on another diffusion process which is driven by a Brownian motion correlated with the one driving the stock price. The agent's preferences are modelled via a CRRA utility function and his objective is to maximize the expected utility of terminal wealth. Employing a novel transformation, we are able to provide closed form solutions for the investor's value function and the optimal portfolio policies. Special cases of the model we develop are the models of portfolio management with stochastic volatility and with nonlinear stock dynamics.