Function Spaces and Capacity Related to a Sublinear Expectation: Application to <Emphasis Type="Italic">G</Emphasis>-Brownian Motion Paths |
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| Authors: | Laurent Denis Mingshang Hu Shige Peng |
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| Institution: | (1) Haskayne School of Business, University of Calgary, Calgary, AB, Canada;(2) Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada;(3) Department of Actuarial Mathematics and Statistics School of Mathematical and Computer Sciences and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK |
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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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