Nonlinear continuous semimartingales
Abstract: In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function that depends on time and path in a non-Markovian way. We provide a dynamic programming principle for the nonlinear expectation and we link the corresponding value function to a variational form of a nonlinear path-dependent partial differential equation. In particular, we establish conditions that allow us to identify the value function as the unique viscosity solution. Furthermore, we prove that the nonlinear expectation solves a nonlinear martingale problem, which confirms our interpretation as a nonlinear semimartingale
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Electronic journal of probability. - 28 (2023) , 1-40, ISSN: 1083-6489
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2024
- Creator
- DOI
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10.1214/23-ejp1037
- URN
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urn:nbn:de:bsz:25-freidok-2536842
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:54 PM CET
Data provider
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Associated
- Criens, David
- Niemann, Lars
- Universität
Time of origin
- 2024
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