Influence of risk tolerance on long-term investments: a Malliavin calculus approach

Abstract

This study investigates the influence of risk tolerance on the expected utility in the long run. We estimate the extent to which the expected utility of optimal portfolios is affected by small changes in the risk tolerance. For this purpose, we adopt the Malliavin calculus method and the Hansen–Scheinkman decomposition, through which the expected utility is expressed in terms of the eigenvalues and eigenfunctions of an operator. We conclude that the influence of risk aversion on the expected utility is determined by these eigenvalues and eigenfunctions in the long run.