Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications

By Shige Peng. 2011

139 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/520f5bcbe5a5de0e789b771e81ec0703adb82aa0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Management Science and Operations Research

Citations in the corpus

Backward stochastic differential equations driven by G-Brownian motion (2012, background): “We refer to a survey paper of [23] for more details of the theoretical studies and applications to, e.”
A martingale approach for fractional Brownian motions and related path dependent PDEs (2017, background): “When g(XT ) is replaced with a more general FXT -measurable random variable ξ and/or X is a non-Markov diffusion process, Yt will depend on the entire path of X up to time t: Yt = u(t,X[0,t]), where X[0,t] := {Xr}0≤r≤t, (1.1) and u solves a so called Path Dependent PDE (PPDE, for short), which was f”
Random G-expectations. (2010, methodology): “For an exhaustive overview of G-expectations and related literature we refer to Peng’s recent ICM paper [16] and survey [15].”
A complete representation theorem for G-martingales (2012, background): “The theory has received very strong attention in the literature in recent years, we refer to the survey paper [20] and the references therein as well as some more recent developments: [4,5,10,12,13,15,16,26], to mention a few.”
Optimal stopping under adverse nonlinear expectation and related games (2012, unknown): “Regarding the literature on nonlinear expectations, we refer to [27, 29] and the references therein; for the related second-order backward stochastic differential equations (2BSDE) to [8, 32, 33], and in particular to [21, 22] for the reflected 2BSDE related to our problem; whereas for the uncertain”
Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012, methodology): “Such equations were firstly proposed by Peng [16] and they provide a convenient language for many problems arising in non-Markovian, or say path dependent framework, with typical examples including martingales, backward stochastic differential equations, second order BSDEs, and backward stochastic P”
Note on Viscosity Solution of Path-Dependent PDE and G-Martingales (2011, background): “It is then a very interesting problem, which was proposed in my lecture of ICM2010 [Peng2010b], whether a path dependent solution of a BSDE and/or a G-martingale can be considered as a nonlinear path-dependent PDE (PPDE) of parabolic and/or elliptic types.”
On viscosity solutions of path dependent PDEs (2011, background): “The present work was largely stimulated by Peng’s recent paper [26], which appeared while our investigation of the problem was in an early stage.”