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The obstacle problem of integro-partial differential equations with applications to stochastic optimal control/stopping problem.
- Source :
-
Journal of the Franklin Institute . Feb2019, Vol. 356 Issue 3, p1396-1423. 28p. - Publication Year :
- 2019
-
Abstract
- Abstract This paper is devoted to existence and uniqueness of minimal mild super solutions to the obstacle problem governed by integro-partial differential equations. We first study the well-posedness and local Lipschitz regularity of Lp solutions (p ≥ 2) to reflected forward-backward stochastic differential equations (FBSDEs) with jump and lower barrier. Then we show that the solutions to reflected FBSDEs provide a probabilistic representation for the mild super solution via a nonlinear Feynman–Kac formula. Finally, we apply the results to study stochastic optimal control/stopping problems. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00160032
- Volume :
- 356
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of the Franklin Institute
- Publication Type :
- Periodical
- Accession number :
- 134447716
- Full Text :
- https://doi.org/10.1016/j.jfranklin.2018.12.005