Asset allocation with time variation in expected returns

This paper analyzes the consumption investment problem of a risk averse investor in continuous time when there are several asset classes. The classic paper in this area is due to Merton who solved the problem when the returns were assumed to be stationary. We assume that there is time variation in the expected returns on the different assets and that this time variation arises from movements in the underlying state variables. We formulate the investorʹs decision as a problem in optimal stochastic control. Our work extends the paper by Brennan et al. (1997) to incorporate a different interest rate process. In addition we investigate the impact of transaction costs on the stock. We employ a viscosity solution approach to the problem and to guarantee a solution we need to impose strong assumptions.