Representation theorems for generators of BSDEs and the extended g-expectations in probability spaces with general filtration

2019/12/10 by Panyu Wu, Guodong Zhang, Wu, Panyu +1
Economics, Econometrics and Finance · Mathematics · #60H10 #60H30 #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1912.04587

openalex publication_date 2019/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we establish representation theorems for generators of backward stochastic differential equations (BSDEs in short) in probability spaces with general filtration from the perspective of transposition solutions of BSDEs. As applications, we give a converse comparison theorem for generators of BSDEs and also some characterizations to positive homogeneity, independence of y, subadditivity and convexity of generators of BSDEs. Then, we extend concepts of g-expectations and conditional g-expectations to the probability spaces with general filtration and investigate their properties.

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