G- Brownian motion and Its Applications

Atena EBRAHIMBEYGI, Elham DASTRANJ
1.866 332

Abstract


Abstract. The concept of G-Brownian motion and G-Ito integral has been introduced by Peng. Also Ito isometry lemma is proved for Ito integral and Brownian motion. In this paper we first investigate the Ito isometry lemma for G-Brownian motion and G-Ito Integral. Then after studying of MG2,0-class functions [4], we introduce Stratonovich integral for G-Brownian motion,say G- Stratonovich integral. Then we present a special construction for G- Stratonovich integral. 


Keywords


G-expectation, G-Brownianmotion, Characterization, Ito integral, G-Stratonovich

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References


Oksendal,B.(2003). Stochastic differential equations (pp20-26). Springer Berlin Heidelberg.

Peng, S. (2006) G–Expectation, G–Brownian Motion and Related Stochastic Calculus of Itˆo’s type, preprint (pdf-file available in arXiv:math.PR/0601035v1 3Jan 2006), to appear in Proceedings of the 2005, Abel Symposium.

Peng, S. (2005), Dynamically consistent nonlinear evaluations and expectations, preprint (pdf-file available in arXiv:math. PR/0501415 v1 24 Jan2005).

Peng, S. (2004) Nonlinear expectation, nonlinear evaluations and risk measurs,in K. Back T. R. Bielecki, C. Hipp, S. Peng, W. Schachermayer, Stochastic Methods in Finance Lectures, 143–217, LNM 1856, Springer-Verlag.

Peng, S. (2004) Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series 20(2), 1–24.