Quadratic Exponential Semimartingales and Application to BSDEs with jumps

Nicole El Karoui (1) , Anis Matoussi (2) , Armand Ngoupeyou

1 UM - Le Mans Université
2 LMM - Laboratoire Manceau de Mathématiques

In this paper, we study a class of Quadratic Backward Stochastic Differential Equations (QBSDE in short) with jumps and unbounded terminal condition. We extend the class of quadratic semimartingales introduced by Barrieu and El Karoui (2013) in the jump diffusion model. The properties of these class of semimartingales lead us to prove existence result for the solution of a quadratic BSDEs.

Mots clés: Backward stochastic differential equation; quadratic semimartingales; un- bounded terminal condition

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Nicole El Karoui, Anis Matoussi, Armand Ngoupeyou. Quadratic Exponential Semimartingales and Application to BSDEs with jumps. 2018. ⟨hal-01740692⟩