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Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

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Abstract

In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov’s criterion for continuous modification of a stochastic process is also obtained. The results can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.

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Authors and Affiliations

  1. Département de Mathématiques, Equipe “Analyse et Probabilités”, Université d’Evry-Val-d’Essonne, Boulevard F. Mitterrand, 91 025, EVRY Cedex, France

    Laurent Denis

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Mingshang Hu & Shige Peng

  3. School of Mathematics, Fudan University, Shanghai, 200433, China

    Shige Peng

Authors
  1. Laurent Denis
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  2. Mingshang Hu
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  3. Shige Peng
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Correspondence to Mingshang Hu.

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Denis, L., Hu, M. & Peng, S. Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths. Potential Anal 34, 139–161 (2011). https://doi.org/10.1007/s11118-010-9185-x

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