Evolution of the Arrow-Pratt Measure of Risk-Tolerance for Predictable Forward Utility Processes

22 Pages Posted: 27 Nov 2018 Last revised: 9 Jun 2020

See all articles by Moris Simon Strub

Moris Simon Strub

Southern University of Science and Technology - Division of Information Systems and Management Engineering

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: November 1, 2018

Abstract

We study the evolution of the Arrow-Pratt measure of risk-tolerance in the framework of discrete-time predictable forward utility (or performance) processes. An agent starts with an initial utility function, which is then sequentially updated forward in time under the guidance of the martingale optimality principle. We first characterize completely the class of forward utility functions that have a time-constant measure of risk-tolerance and thus a preservation of preferences. We then show that, in general, preferences vary over time and whether the agent becomes more or less tolerant to risk is related to the curvature of the measure of risk-tolerance. An example where the initial utility function belongs to the SAHARA class, which is found to be analytically tractable and stable in the sense that all the subsequent utility functions belong to the same class as the initial one, illustrates the obtained results.

Keywords: Risk-aversion, Arrow-Pratt measure of risk-tolerance, forward utility (performance) processes, dynamic preferences, portfolio selection, binomial model, SAHARA utility

JEL Classification: G11, C61

Suggested Citation

Strub, Moris Simon and Zhou, Xunyu, Evolution of the Arrow-Pratt Measure of Risk-Tolerance for Predictable Forward Utility Processes (November 1, 2018). Available at SSRN: https://ssrn.com/abstract=3276638 or http://dx.doi.org/10.2139/ssrn.3276638

Moris Simon Strub (Contact Author)

Southern University of Science and Technology - Division of Information Systems and Management Engineering ( email )

1088 Xueyuan Ave
Shenzhen, Guangdong
China

HOME PAGE: http://sites.google.com/view/morisstrub/home

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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