Reflected solutions of backward stochastic differential equations driven by G-Brownian motion

Hanwu Li (1) , Shige Peng (1) , Abdoulaye Soumana-Hima (2, 3)

1 Shandong University
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Département de Mathématiques - Université de Maradi

In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion. The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a “martingale condition” instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization. We then give some applications including a generalized Feynman-Kac formula of an obstacle problem for fully nonlinear partial differential equation and option pricing of American types under volatility uncertainty.

Mots clés: G-expectation; reflected bacward stochastic differential equations; obstacle problems for fully nonlinear PDEs

Domaines: Probabilités [math.PR]

Hanwu Li, Shige Peng, Abdoulaye Soumana-Hima. Reflected solutions of backward stochastic differential equations driven by G-Brownian motion. Science China Mathematics, 2018, 61 (1), pp.1 - 26. ⟨10.1007/s11425-017-9176-0⟩. ⟨hal-01731309⟩