Optimal Stopping for Exponential Lévy Models with Weighted Discounting

David Landriault, Bin Li, Jose M. Pedraza Ramirez

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Abstract

This paper considers an optimal stopping problem with weighted discounting, and the state process is modeled by a general exponential L\'evy process. Due to the time inconsistency, we provide a new martingale method based on a verification theorem for the equilibrium stopping strategies. As an application, we generalize an investment problem with non-exponential discounting studied by Grenadier and Wang (J. Financ. Econom., 84 (2007), pp. 2--39) and Ebert, Wei, and Zhou (J. Econom. Theory, 189 (2020), 105089) to L\'evy models. Closed-form equilibrium stopping strategies are derived, which are closely related to the running maximum of the state process. The impacts of discounting preferences on the equilibrium stopping strategies are examined analytically.
Original languageEnglish
Pages (from-to)777-811
Number of pages35
JournalSIAM Journal on Financial Mathematics
Volume14
Issue number3
Early online date13 Jul 2023
DOIs
Publication statusPublished - 1 Sept 2023

Keywords

  • L'evy processes
  • optimal stopping
  • time inconsistency
  • weighted discounting

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