Stability and Markov Property of Forward Backward Minimal Supersolutions

Authors

Samuel Drapeau and Christoph Mainberger

Date

2016

Journal

Electronic Journal of Probability, 21(41):1–15

Abstract

We show stability and locality of the minimal supersolution of a forward backward stochastic differential equation with respect to the underlying forward process under weak assumptions on the generator. The forward process appears both in the generator and the terminal condition. Painlevé-Kuratowski and Convex Epi-convergence are used to establish the stability. For Markovian forward processes the minimal supersolution is shown to have the Markov property. Furthermore, it is related to a time-shifted problem and identified as a viscosity supersolution of a corresponding PDE.

Keywords

Supersolutions of Backward Stochastic Differential Equations, Stability, FBSDEs, Markov Property, Viscosity Supersolutions

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