322 citations · 795 across the 14 of their papers we have counts for
5 papers · 2 filters
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…
Mean-field backward stochastic differential equations: A limit approach
Rainer Buckdahn, Boualem Djehiche, Juan Li +1
Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance…
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…