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