Extended Conditional G-Expectations and Related Stopping Times

2013/09/16 by Mingshang Hu, Hu, Mingshang, Shigē Péng +1 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · #60H10 #60H30 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1309.3829

openalex publication_date 2013/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we extend the definition of time conditional G-expectations \mathbbE_t[⋅] to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time conditional expectations for each random variable X which is the downward limit (resp. upward limit) of a monotone sequence \X_i\ in L_G¹(Ω). To accomplish this procedure, some careful analysis is needed. Moreover, we give a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional G-expectations.

Cited by

• A Parametric Methodology for G-Expectations and Stochastic Systems under Model Uncertainty
• Reflected Solutions of BSDEs Driven by G-Brownian Motion
• Optimal Stopping under G-expectation

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