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Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting

Authors
  • Marushkevych, Dmytro1
  • Popier, Alexandre1
  • 1 Laboratoire Manceau de Mathématiques, Le Mans Université, Avenue Olivier Messiaen, Le Mans cedex 9, 72085, France , Le Mans cedex 9 (France)
Type
Published Article
Journal
Probability, Uncertainty and Quantitative Risk
Publisher
Springer Singapore
Publication Date
Feb 19, 2020
Volume
5
Issue
1
Identifiers
DOI: 10.1186/s41546-020-0043-5
Source
Springer Nature
Keywords
License
Green

Abstract

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminft→TY(t)=ξ=Y(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\liminf _{t\to T} Y(t) = \xi = Y(T)$\end{document}. Hence, we extend known results for a non-Markovian terminal condition.

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