An Inverse Optimal Stopping Problem for Diffusion Processes

Thomas Kruse () and Philipp Strack ()
Additional contact information
Thomas Kruse: University of Duisburg-Essen, 45127 Essen, Germany

Mathematics of Operations Research, 2019, vol. 44, issue 2, 423-439

Abstract: Let X be a one-dimensional diffusion and let g be a real-valued function depending on time and the value of X . This article analyzes the inverse optimal stopping problem of finding a time-dependent real-valued function π depending only on time such that a given stopping time τ ⋆ is a solution of the stopping problem sup τ 𝔼 [ g ( τ , X τ ) + π ( τ ) ] .

Under regularity and monotonicity conditions, there exists such a transfer π if and only if τ ⋆ is the first time when X exceeds a time-dependent barrier b . We prove uniqueness of the solution π and derive a closed form representation. The representation is based on an auxiliary process that is a version of the original diffusion X reflected at b towards the continuation region. The results lead to a new integral equation characterizing the stopping boundary b of the stopping problem sup τ 𝔼 [ g ( τ , X τ ) ] .

Keywords: optimal stopping; reflected stochastic processes; dynamic mechanism design; dynamic implementability (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1287/moor.2018.0930 (application/pdf)

Related works:
Working Paper: An inverse optimal stopping problem for diffusion processes (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:44:y:2019:i:2:p:423-439

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().