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
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Anmerkungen
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Electronic journal of probability. - 28 (2023) , 1-40, ISSN: 1083-6489
- Ereignis
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Veröffentlichung
- (wo)
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Freiburg
- (wer)
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Universität
- (wann)
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2024
- Urheber
- DOI
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10.1214/23-ejp1037
- URN
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urn:nbn:de:bsz:25-freidok-2536842
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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14.08.2025, 07:46 MESZ
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Beteiligte
- Criens, David
- Niemann, Lars
- Universität
Entstanden
- 2024
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