A stochastic control problem and related free boundaries in finance

Chonghu Guan, Xun Li, Zuoquan Xu, Fahuai Yi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

In this paper, we investigate an optimal stopping problem (mixed with stochastic controls) for a manager whose utility is nonsmooth and nonconcave over a finite time horizon. The paper aims to develop a new methodology, which is significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, so as to figure out the manager’s best strategies. The problem is first reformulated into a free boundary problem with a fully nonlinear operator. Then, by means of a dual transformation, it is further converted into a free boundary problem with a linear operator, which can be consequently tackled by the classical method. Finally, using the inverse transformation, we obtain the properties of the optimal trading strategy and the optimal stopping time for the original problem.
Original languageEnglish
Pages (from-to)563-584
Number of pages22
JournalMathematical Control and Related Fields
Volume7
Issue number4
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Dual transformation
  • Free boundary
  • Nonsmooth utility
  • Optimal stopping
  • Parabolic variational inequality

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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