On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion

2009/04/29 by Mingshang Hu, Hu, Mingshang, Shigē Péng +1 · 4 citations
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60E05 #60E07 #60H05 #60H10 #60H30 #62C05 #62D05 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0904.4519

openalex publication_date 2009/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures \P_θ:θ∈ Θ\ to represent an important sublinear expectation--G-expectation 𝔼[⋅]. We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions L_ip(Ω) in order to prove that C_b(Ω) belongs to the 𝔼[|⋅|]-completion of the L_ip(Ω).

Citations

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

Cited by

• Stochastic PDEs driven by G-Brownian motion and the associated Backward Doubly Stochastic Differential Equations
• Pathwise Patching: A Geometric Construction of Quasi-Sure Solutions to G-SDEs
• Squared Bessel processes under nonlinear expectation
• A Parametric Methodology for G-Expectations and Stochastic Systems under Model Uncertainty

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