Optimal redeeming strategy of stock loans under drift uncertainty

Zuo Quan Xu, Fahuai Yi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull or bear) trends of the underlying stock. This is called drift uncertainty. Owing to the unavoidable need for the estimation of trends while making decisions, the related Hamilton–Jacobi–Bellman equation turns out to be of a degenerate parabolic type. Hence, it is very hard to obtain its regularity using the standard approach, making the problem different from the existing optimal redeeming problems without drift uncertainty. We present a thorough and delicate probabilistic and functional analysis to obtain the regularity of the value function and the optimal redeeming strategies. The optimal redeeming strategies of stock loans appear significantly different in the bull and bear trends.

Original languageEnglish
Pages (from-to)384-401
Number of pages18
JournalMathematics of Operations Research
Issue number1
Publication statusPublished - 1 Feb 2020


  • Bull and bear trends
  • Degenerate parabolic variational inequality
  • Drift uncertainty
  • Optimal stopping
  • Stock loan

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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