Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence

62 Pages Posted: 30 Jul 2021

See all articles by Jing Guo

Jing Guo

Columbia University - Fu Foundation School of Engineering and Applied Science

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Date Written: June 19, 2019

Abstract

We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses. We also study the utility process in this generalized model with constant elasticity of intertemporal substitution and relative risk aversion degree, and with infinite time horizon. In a specific, finite-state Markovian setting, we prove that the utility process uniquely exists when the agent derives nonnegative gain-loss utility, and that it can be non-existent or non-unique otherwise. Moreover, we prove that the utility process, when it uniquely exists, can be computed by starting from any initial guess and applying the recursive equation that defines the utility process repeatedly. We then consider a portfolio selection problem with gain-loss utility and solve it by proving that the corresponding dynamic programming equation has a unique solution. Finally, we extend certain previous results to the case in which the state space is infinite.

Keywords: recursive utility, gains and losses, existence and uniqueness, Markov processes, portfolio selection, dynamic programming

JEL Classification: G02, G11

Suggested Citation

Guo, Jing and He, Xue Dong, Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence (June 19, 2019). Available at SSRN: https://ssrn.com/abstract=2790768 or http://dx.doi.org/10.2139/ssrn.2790768

Jing Guo

Columbia University - Fu Foundation School of Engineering and Applied Science ( email )

New York, NY
United States

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
208
Abstract Views
1,224
Rank
220,388
PlumX Metrics