G-Brownian Motion - Brownian Motion with Variance Uncertainty


Julian Hollender (TU Dresden)
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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).

講 師:
Julian Hollender (TU Dresden)
テーマ:
G-Brownian Motion - Brownian Motion with Variance Uncertainty
日 時:
2014年10月10日(金)16:50-17:50
場 所:
大阪大学大学院基礎工学研究科 (豊中キャンパス)I 棟 204号室
参加費:
無料
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