Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths
Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths
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DOI：
10.1007/s11118-010-9185-x
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发表时间：
2008-02
影响因子：
1.1
通讯作者：
L. Denis;Mingshang Hu;S. Peng
中科院分区：
文献类型：
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作者：
L. Denis;Mingshang Hu;S. Peng
本文给出了由次线性期望- g期望诱导的g -布朗运动路径函数的几个典型巴纳赫空间的一些基本和重要性质。许多结果也可以应用于更一般的情况。给出了随机过程连续修正的广义Kolmogorov准则。研究结果可应用于金融领域连续时间动态和连贯的风险度量，特别是在波动率模型不确定性情况下的路径依赖风险头寸。
In this paper we give some basic and important properties of several typical Banach spaces of functions ofG-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.