Backward stochastic differential equations driven by G-Brownian motion

By Mingshang Hu, Shaolin Ji, Shige Peng, Yongsheng Song. 2012

186 citations recorded by the source corpus.

In this paper, we study the backward stochastic differential equations driven by a G-Brownian motion (Bt)t≥0 in the following form: Yt=ξ+∫tTf(s,Ys,Zs)ds+∫tTg(s,Ys,Zs)d〈B〉s−∫tTZsdBs−(KT−Kt), where K is a decreasing G-martingale. Under Lipschitz conditions of f and g in Y and Z, the existence and uniqueness of the solution (Y,Z,K) of the above BSDE in the G-framework is proved.

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/b294f1ac1b487f46ed655ddf268d9afc16c991a3

How researchers see this paper

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In Applied Mathematics

1. Jianfeng Zhang
2. Nizar Touzi
3. Shige Peng
4. Mingshang Hu
5. Ibrahim Ekren
6. Xiaolu Tan
7. Shaolin Ji
8. Falei Wang

In Finance

1. Jianfeng Zhang
2. Marcel Nutz
3. Nizar Touzi
4. Shige Peng
5. Yongsheng Song
6. Mingshang Hu
7. Ibrahim Ekren
8. Shaolin Ji

In Modeling and Simulation

1. Jianfeng Zhang
2. Yongsheng Song
3. Nizar Touzi
4. Mingshang Hu
5. Xue-peng Bai
6. Yiqing Lin
7. Ibrahim Ekren
8. Dylan Possamaï

Citations in the corpus

• Quasi-continuous random variables and processes under the G-expectation framework (2014, result): “In particular, by slightly more involved estimates, our results still hold for the following PDE (see [3, 4]):”
• Stochastic control for a class of nonlinear kernels and applications (2015, background): “We also would like to mention a related theory developed around the notion of G−expectations introduced by Peng [70], which lead to the so-called G−BSDEs (see [44, 45]).”
• On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients (2010, background): “Subsequently, Hu et al.([5]) have derived a complete existence and uniqueness theorem for nonlinear GBSDEs with a generator f that is uniformly Lipschitz in both y and z.”
• 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.”
• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion (2012, background): “ ηiIAi : Ai ∈ B(Ωt),ηi ∈ L p G(Ω),n∈ N}, we define the corresponding conditional G-expectation, still denoted by Eˆs[·], by setting Eˆ s[ Xn i=1 ηiIAi] := Xn i=1 Eˆ s[ηi]IAi for s≥ t. Proposition 2.8 ([7]) For each ξ,η∈ L0,1,t G (ΩT ), we have (i) Monotonicity: If ξ≤ η, then Eˆs[ξ] ≤ Eˆs[η] for any s”
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012, background): “See also the closely related works [16, 24] in terms of the G-expectation.”