322 citations · 795 across the 14 of their papers we have counts for
5 papers · 2 filters
Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition
Shige Peng, Mingyu Xu
In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decompositi…
Numerical Algorithms for 1-d Backward Stochastic Differential Equations: Convergence and Simulations
Shige Peng, Mingyu Xu
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implic…
Modelling Derivatives Pricing Mechanisms with Their Generating Functions
Shige Peng
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a back…
Multi-Dimensional G-Brownian Motion and Related Stochastic Calculus under G-Expectation
Shige Peng
We develop a notion of nonlinear expectation --G-expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal dist…
G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type
Shige Peng
We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard n…