Nonconcave Utility Maximization with Portfolio Bounds

• 成果类型: Article
• 署名作者: Dai, Min; Kou, Steven; Qian, Shuaijie; Wan, Xiangwei
• 署名单位: Hong Kong Polytechnic University; National University of Singapore; National University of Singapore; Boston University; National University of Singapore; Shanghai Jiao Tong University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2021.4228
• 发表日期: 2022
• 页码: 8368-8385
• 关键词: PORTFOLIO CONSTRAINTS; behavioral economics; incentive schemes; concavification principle

摘要

The problems of nonconcave utility maximization appear in many areas of finance and economics, such as in behavioral economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving nonconcave utility maximization problems, where the concavification principle may not hold, and the utility functions can be discontinuous. We find that adding portfolio bounds can offer distinct economic insights and implications consistent with existing empirical findings. Theoretically, by introducing a new definition of viscosity solution, we show that a monotone, stable, and consistent finite difference scheme converges to the value functions of the nonconcave utility maximization problems.