Nonconcave Utility Maximization with Portfolio Bounds

Min Dai, Steven Kou, Shuaijie Qian, Xiangwei Wan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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 consistentwith 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 utilitymaximization problems.

Original languageEnglish
Pages (from-to)8368-8385
Number of pages18
JournalManagement Science
Issue number11
Publication statusPublished - Nov 2022


  • behavioral economics
  • concavification principle
  • incentive schemes
  • portfolio constraints

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research


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