Investment Strategies in Incomplete Markets : Sufficient Conditions for a Closed Form Solution

This paper analyses the portfolio problem of an investor who wants to maximize the expected power utility of his terminal wealth both in a complete and an incomplete financial market. We derive sufficient conditions for having a closed form solution. These conditions must hold on a suitable combination of the drift and diffusion coefficients of the stochastic processes describing the state variables and the asset prices. In particular, we show that our framework leads to two cases : (i) the case solvable thorough a log-linear value fucntion, and (ii) the case solvable thorough a log quadratie value function.