Dynamic Investment, Risk Aversion, and Foresight Sensitivity

Since optimal investment strategies generally cannot be obtained in closed form when consumers exhibit non-constant risk aversion, many dynamic investment studies have focused on the constant risk aversion case. This study considers a general class of dynamic investment models in which agents are not restricted to have constant risk aversion. Existence, monotonicity, concavity, differentiability, and absolute risk aversion properties are established analytically for the optimal feedback investment strategies and dynamic progamming value functions. A bound is also obtained on the loss in expected utility resulting from the use of limited foresight horizons. Finally, results are reported for computer experiments conducted to explore the sensitivity of expected utility outcomes to changes in the length of the foresight horizon. For example, the results indicate the optimality of a rolling 2-period foresight horizon for a particular class of exponential utility functions exhibiting decreasing risk aversion. Annotated pointers to related work can be accessed here: http://www.econ.iastate.edu/tesfatsi/dehome.htm