Nonlinear Expectations and Stochastic Calculus under Uncertainty

2010/02/24 by Shigē Péng, Peng, Shige · 18 citations
Decision Sciences · #60E05 #60E07 #60H05 #60H10 #60H30 #62C05 #62D05 #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1002.4546

openalex publication_date 2010/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under sublinear expectation. We also present a new type of Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide robust tools for the problem of probability model uncertainty arising from financial risk management, statistics and stochastic controls.

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