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Optimal stopping of BSDEs with constrained jumps and related zero-sum games
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-3111-4820
2024 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 173, article id 104355Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a penalization technique and the primary challenge we encounter is demonstrating the regularity of the limit for the scheme. Additionally, we relate the Snell envelope to a finite horizon, zero-sum stochastic differential game, where one player controls a path-dependent stochastic system by invoking impulses, while the opponent is given the opportunity to stop the game prematurely. Importantly, by developing new techniques within the realm of control randomization, we demonstrate that the value of the game exists and is precisely characterized by our non-linear Snell envelope.

Place, publisher, year, edition, pages
Elsevier, 2024. Vol. 173, article id 104355
National Category
Probability Theory and Statistics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-129789DOI: 10.1016/j.spa.2024.104355ISI: 001230030900001Scopus ID: 2-s2.0-85190241469OAI: oai:DiVA.org:lnu-129789DiVA, id: diva2:1863572
Funder
Swedish Energy Agency, P2020-90032Available from: 2024-05-31 Created: 2024-05-31 Last updated: 2024-06-03Bibliographically approved

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Perninge, Magnus

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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