Nonlinear semimartingales and Markov processes with jumps
Abstract: In this paper, we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics, which are prescribed by a time and path-dependent set-valued function. We show that the associated control problem coincides with both its weak and relaxed counterparts. Furthermore, we establish regularity properties of the value function and discuss their relation to Feller properties of sublinear semigroups. In the Markovian case, we provide conditions that allow us to identify the corresponding semigroup as the unique viscosity solution to a nonlinear Hamilton–Jacobi–Bellman equation. To illustrate our results, we discuss a random G-double exponential Lévy setting
- 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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Journal of evolution equations. - 25, 1 (2025) , 21, ISSN: 1424-3202
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2025
- Creator
- DOI
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10.1007/s00028-024-01046-6
- URN
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urn:nbn:de:bsz:25-freidok-2624345
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:32 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Criens, David
- Niemann, Lars
- Universität
Time of origin
- 2025
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