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

TL;DR

This paper uses advanced mathematical techniques to analyze how risk tolerance impacts long-term expected utility in investment portfolios, revealing that eigenvalues and eigenfunctions govern this influence.

Contribution

It introduces a novel application of Malliavin calculus and Hansen--Scheinkman decomposition to study risk tolerance effects in long-term investments.

Findings

Eigenvalues and eigenfunctions determine the influence of risk aversion.

Expected utility is affected by small changes in risk tolerance.

Method provides a new analytical framework for long-term investment analysis.

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.