• Medientyp: E-Artikel
  • Titel: Nonlinear continuous semimartingales
  • Beteiligte: Criens, David [Verfasser:in]; Niemann, Lars [Verfasser:in]
  • Erschienen: University of Freiburg: FreiDok, 2023
  • Erschienen in: Electronic journal of probability. - 28 (2023) , 1-40, ISSN: 1083-6489
  • Sprache: Englisch
  • DOI: https://doi.org/10.1214/23-ejp1037
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  • Beschreibung: 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.
  • Zugangsstatus: Freier Zugang