On the time consistent solution to optimal stopping problems with expectation constraint

2023/11/09 by Sören Christensen, Christensen, Sören, Maike Klein +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #60G40 #60J70 #91A25 #91B51 #Auction Theory and Applications #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2311.05378

openalex publication_date 2023/11/09 · openalex created_date 2023/11/11 · openalex updated_date 2026/07/28

Abstract

We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of randomized but purely state dependent stopping times as admissible strategies. We derive a verification theorem and necessary conditions for equilibria, which together basically characterize all equilibria. Furthermore, additional structural properties of equilibria are obtained to feed a possible guess-and-verify approach, which is then illustrated by an example.

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