Optimal stopping under model ambiguity: A time-consistent equilibrium approach

Yu Jui Huang, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an (Formula presented.) -maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. For a one-dimensional diffusion with drift and volatility uncertainty, we show that any initial stopping policy will converge to an equilibrium through a fixed-point iteration. This allows us to capture much more diverse behavior, depending on an agent's ambiguity attitude, beyond the standard worst-case (or best-case) analysis. In a concrete example of real options valuation under model ambiguity, all equilibrium stopping policies, as well as the best one among them, are fully characterized under appropriate conditions. It demonstrates explicitly the effect of ambiguity attitude on decision making: the more ambiguity-averse, the more eager to stop—so as to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established.

Original languageEnglish
Pages (from-to)979-1012
Number of pages34
JournalMathematical Finance
Volume31
Issue number3
Early online dateApr 2021
DOIs
Publication statusPublished - Jul 2021

Keywords

  • ambiguity attitude
  • equilibrium stopping policies
  • generalized measurable projection theorem
  • model ambiguity
  • optimal stopping
  • real options valuation
  • time inconsistency

ASJC Scopus subject areas

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics

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