Dynkin Games for Lévy Processes

Fuente: arXiv
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Bibliographic Details
Main Authors: Aspirot, Laura, Mordecki, Ernesto, Sosa, Andres
Format: Preprint
Published: 2024
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author Aspirot, Laura
Mordecki, Ernesto
Sosa, Andres
author_facet Aspirot, Laura
Mordecki, Ernesto
Sosa, Andres
contents We obtain a verification theorem for solving a Dynkin game driven by a Lévy process. The result requires finding two averaging functions that, composed respectively with the supremum and the infimum of the process, summed, and taked the expectation, provide the value function of the game. The optimal stopping rules are the respective hitting times of the support sets of the averaging functions. The proof relies on fluctuation identities of the underlying Lévy process. We illustrate our result with three new simple examples, where the smooth pasting property of the solutions is not always present.
format Preprint
id arxiv_https___arxiv_org_abs_2410_23509
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Dynkin Games for Lévy Processes
Aspirot, Laura
Mordecki, Ernesto
Sosa, Andres
Probability
60G40, 60G51, 91A15
We obtain a verification theorem for solving a Dynkin game driven by a Lévy process. The result requires finding two averaging functions that, composed respectively with the supremum and the infimum of the process, summed, and taked the expectation, provide the value function of the game. The optimal stopping rules are the respective hitting times of the support sets of the averaging functions. The proof relies on fluctuation identities of the underlying Lévy process. We illustrate our result with three new simple examples, where the smooth pasting property of the solutions is not always present.
title Dynkin Games for Lévy Processes
topic Probability
60G40, 60G51, 91A15
url https://arxiv.org/abs/2410.23509