Martingale driven BSDEs, PDEs and other related deterministic problems

Adrien Barrasso (1, 2) , Francesco Russo (1)

1 UMA - Unité de Mathématiques Appliquées
2 X - École polytechnique

We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.

Mots clés: Decoupled mild solutions; Martingale problem; cadlag martingale; pseudo-PDE; Markov processes; backward stochastic differential equation

Domaines: Probabilités [math.PR]

Adrien Barrasso, Francesco Russo. Martingale driven BSDEs, PDEs and other related deterministic problems. 2017. ⟨hal-01566883v1⟩