An optimal investment problem with nonsmooth and nonconcave utility over a finite time horizon

Chonghu Guan, Xun Li, Wenxin Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review


In this paper, we study a class of optimal investment problems with a nonsmooth and nonconcave utility function, where the value function is the expected utility determined by the state process and time. We adopt partial differential equation methods to prove that the value function belongs to C2,1 under some proper conditions of the utility function. Moreover, we analyze the continuity of the optimal strategy and obtain some of its properties around the boundary and the terminal time. Also, an example sheds light on the theoretical results established.

Original languageEnglish
Pages (from-to)411-436
Number of pages26
JournalSIAM Journal on Financial Mathematics
Issue number2
Publication statusPublished - 23 Apr 2020


  • Dual transformation
  • Nonconcave
  • Nonsmooth
  • Optimal investment
  • Parabolic quasi-linear equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics

Cite this