Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs

Abstract

In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.

39 pages

References in corpus (3)

• Constructing Sublinear Expectations on Path Space
• Measurability of Semimartingale Characteristics with Respect to the Probability Law
• Second Order Backward Stochastic Differential Equations with Quadratic Growth

Cited by in corpus (2)

• Second-order BSDEs with jumps: Formulation and uniqueness
• Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity