An inverse optimal stopping problem for diffusion processes

Thomas Kruse and Philipp Strack ()

Papers from arXiv.org

Abstract: Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function $\pi:[0,T]\to\mathbb{R}$ such that a given stopping time $\tau^{\star}$ is a solution of the stopping problem $\sup_{\tau}\mathbb{E}\left[g(\tau,X_{\tau})+\pi(\tau)\right]\,.$ Under regularity and monotonicity conditions, there exists a solution $\pi$ if and only if $\tau^{\star}$ is the first time when $X$ exceeds a time-dependent barrier $b$, i.e. $\tau^{\star}=\inf\left\{ t\ge0\,|\,X_{t}\ge b(t)\right\} \,.$ We prove uniqueness of the solution $\pi$ and derive a closed form representation. The representation is based on an auxiliary process which 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 $\sup_{\tau}\mathbb{E}\left[g(\tau,X_{\tau})\right]$.

Date: 2014-06, Revised 2017-08
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/1406.0209 Latest version (application/pdf)

Related works:
Journal Article: An Inverse Optimal Stopping Problem for Diffusion Processes (2019)
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:arx:papers:1406.0209

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().