大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

G-Brownian Motion - Brownian Motion with Variance Uncertainty

Julian Hollender (TU Dresden)

1. ホーム
2. セミナー・集中講義
3. セミナー
4. G-Brownian Motion - Brownian Motion with Variance Uncertainty

大阪大学 金融・保険セミナーシリーズ 第55回(CSFI-阪大確率論セミナー共催)

G-Brownian Motion - Brownian Motion with Variance Uncertainty

Julian Hollender (TU Dresden)

We will discuss the notion of nonlinear expectation spaces and related results, to introduce Brownian motion under volatility uncertainty as in [1]. This so-called G-Brownian motion and the canonical pathspace G-expectation have a strong connection to certain nonlinear second-order partial differential equations, which allow us to evaluate risk bounds for applications with distributional uncertainty. Even more, it is possible to formulate and solve important problems, such as SDEs or BSDEs, with respect to G-Brownian motion, c.f. for example [2] or [3]. The aim of this talk is to present the involved concepts and to give an overview over possible applications.

[1] Peng, Shige. "G-expectation, G-Brownian motion and related stochastic calculus of Ito type." Stochastic analysis and applications. Springer Berlin Heidelberg, 2007. 541-567.

[2] Hu, Ze-Chun, and Ling Zhou. "Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations." arXiv preprint arXiv:1211.1090 (2012).

[3] Zheng, Zhonghao, Xiuchun Bi, and Shuguang Zhang. "Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion." arXiv preprint arXiv:1306.0176 (2013).