Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

2008/02/09 by Laurent Denis, Denis, Laurent, Mingshang Hu +4 · 20 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #31A15 #60G05 #60G17 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #msc:31A15 #msc:60G05 #msc:60G17

paper · pdf · doi:10.48550/arxiv.0802.1240

26 pages

openalex publication_date 2008/02/09 · arxiv created 2010/01/15 · arxiv updated 2010/02/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion pathes 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 to 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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