168 citations · 460 across the 9 of their papers we have counts for
5 papers · 1 filter
Constrained BSDE and Viscosity Solutions of Variation Inequalities
Shige Peng, Mingyu Xu
In this paper, we study the relation between the smallest -supersolution of constraint backward stochastic differential equation and viscosity solution of constraint semilineare…
G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
Shige Peng
We introduce a new notion of G-normal distributions. This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) thro…
Mean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations
Rainer Buckdahn, Juan Li, Shige Peng
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as lim…
Representation Theorems for Quadratic -Consistent Nonlinear Expectations
Ying Hu, Jin Ma, Shige Peng +1
In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "-consistent nonlinear expectation") to the case when it is allowed to be dominat…
Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations
Shige Peng
The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertain…