Non-Concave Utility Maximization without the Concavification Principle

64 Pages Posted: 19 Jul 2019 Last revised: 3 Sep 2019

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Steven Kou

Boston University

Shuaijie Qian

National University of Singapore (NUS)

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Date Written: July 18, 2019

Abstract

The problems of non-concave utility maximization appear in many areas of finance and economics, such as in behavior economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving non-concave utility maximization problems, where the concavification principle may not hold and the utility functions can be discontinuous. In particular, we find that adding bounded portfolio constraints, which makes the concavification principle invalid, can significantly affect economic insights in the existing literature. Theoretically, we give a new definition of viscosity solution and show that a monotone, stable, and consistent finite difference scheme converges to the solution of the utility maximization problem.

Keywords: Non-Concave Utility, Portfolio Constraints, Discontinuous Viscosity Solution

JEL Classification: G11, D91, C61, G23

Suggested Citation

Dai, Min and Kou, Steven and Qian, Shuaijie and Wan, Xiangwei, Non-Concave Utility Maximization without the Concavification Principle (July 18, 2019). Available at SSRN: https://ssrn.com/abstract=3422276 or http://dx.doi.org/10.2139/ssrn.3422276

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Steven Kou

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
6173583318 (Phone)

Shuaijie Qian

National University of Singapore (NUS) ( email )

Bukit Timah Road 469 G
Singapore, 117591
Singapore

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management ( email )

No.1954 Huashan Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200030
China
+86-21-52301570 (Phone)

HOME PAGE: http://sites.google.com/view/wanxiangwei/research

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