Open Access
August 2020 Conditional optimal stopping: A time-inconsistent optimization
Marcel Nutz, Yuchong Zhang
Ann. Appl. Probab. 30(4): 1669-1692 (August 2020). DOI: 10.1214/19-AAP1540


Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time of stopping, or a company may condition on not being bankrupt. We observe that conditional optimization is time-inconsistent due to the dynamic change of the conditioning probability and develop an equilibrium approach in the spirit of R. H. Strotz’ work for sophisticated agents in discrete time. Equilibria are found to be essentially unique in the case of a finite time horizon whereas an infinite horizon gives rise to nonuniqueness and other interesting phenomena. We also introduce a theory which generalizes the classical Snell envelope approach for optimal stopping by considering a pair of processes with Snell-type properties.


Download Citation

Marcel Nutz. Yuchong Zhang. "Conditional optimal stopping: A time-inconsistent optimization." Ann. Appl. Probab. 30 (4) 1669 - 1692, August 2020.


Received: 1 January 2019; Revised: 1 October 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4133380
Digital Object Identifier: 10.1214/19-AAP1540

Primary: 60G40 , 91A13 , 91A15 , 93E20

Keywords: Conditional optimal stopping , Equilibrium , time-inconsistency

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 4 • August 2020
Back to Top