The Exact Solution of Multi-period Portfolio Choice Problem with Exponential Utility

Abstract

In the current paper we derive the exact analytical solution of the multi-period portfolio choice problem for an exponential utility function. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns follows a vector autoregression. We prove that the optimal portfolio weights depend on the covariance matrices of the next two periods and the conditional mean vector of the next period. The case without predictable variables and the case of independent asset returns are partial cases of our solution.