An Optimal Stochastic Investment and Consumption Strategy with Log Utility

Abstract

This paper considers a single investor who owns a production plant that generates units of consumption goods in a capitalist economy. The goal is to choose optimal investment and consumption policies that maximize the finite horizon expected discounted logarithmic utility of consumption and terminal wealth. A dynamical programming principle is used to derive the optimal investment and consumption strategy when the state variable follows a meanreverting square root process.

Keywords: Mean-reverting square root process, Control process, Optimal Strategies, Dynamic Programming Principle