Dynamic investment, risk aversion, and foresight sensitivity

Abstract

Since optimal investment strategies generally cannot be obtained in closed form when utility functions exhibit non-constant risk aversion, most dynamic investment studies have focused on the constant risk aversion case. The present paper investigates a general class of dynamic investment models with final-period expected wealth objective for which the final-period utility of wealth function is not restricted to be constantly risk averse. Existence, monotonicity, concavity, differentiability, and absolute risk aversion properties are established for the optimal feedback investment strategies and dynamic programming indirect utility functions. The loss in final-period expected utility resulting from the use of limited foresight investments is shown to be bounded above by terms dependent both on the variance of myopically achievable utility and on the relative size of myopic and global absolute risk aversion. Finally, simulation results are presented which indicate the optimality of a rolling 2-period foresight horizon for a class of exponential utility functions exhibiting decreasing absolute risk aversion.