Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations

Adrien Barrasso (1) , Francesco Russo (2)

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

We investigate existence and uniqueness for a new class of Backward Stochastic Differential Equations (BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process X those BSDEs are denominated forward BSDEs and can be associated to a deter-ministic problem, called Pseudo-PDE which constitute the natural generalization of a parabolic semilinear PDE which naturally appears when the underlying filtration is Brownian. We consider two types of solutions for the Pseudo-PDEs: classical and of martingale type.

Mots clés: Martingale problem; pseudo-PDE; Markov processes; backward stochastic differential equation.

Domaines: Probabilités [math.PR]

Adrien Barrasso, Francesco Russo. Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations: Backward Stochastic Differential Equations with no driving martingale. 2017. ⟨hal-01431559v1⟩