Risk Aversion and Portfolio Selection in a Continuous-Time Model

TL;DR

This paper analyzes how risk aversion influences optimal portfolio choices in a continuous-time market, showing that more risk-averse investors allocate less wealth to risky assets based on utility function properties.

Contribution

It demonstrates the relationship between risk aversion and portfolio allocation in a continuous-time setting with deterministic coefficients, extending existing models.

Findings

More risk-averse agents invest less in risky assets.

Indirect utility functions reflect the order of risk aversion.

Portfolio choices depend on the risk aversion level.

Abstract

The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. It turns out that the indirect utility functions inherit the order of risk aversion (in the Arrow-Pratt sense) from the von Neumann-Morgenstern utility functions, and therefore, a more risk-averse agent would invest less wealth (in absolute value) in the risky assets.