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An Inverse Optimal Stopping Problem for Diffusion Processes

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  • Thomas Kruse

    (University of Duisburg-Essen, 45127 Essen, Germany)

  • Philipp Strack

    (University of California, Berkeley, Berkeley, California 94720)

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 ) ] .

Suggested Citation

  • Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    • Handle: RePEc:inm:ormoor:v:44:y:2019:i:2:p:423-439
    DOI: 10.1287/moor.2018.0930
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    Cited by:

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    3. Marco Buso & Cesare Dosi & Michele Moretto, 2018. "Termination Fees and Contract Design in Public-Private Partnerships," "Marco Fanno" Working Papers 0227, Dipartimento di Scienze Economiche "Marco Fanno".

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