Convexity and sublinearity of g-expectations

Ronglin Ji, Xuejun Shi, Shijie Wang and Jinming Zhou

Statistics & Probability Letters, 2022, vol. 189, issue C

Abstract: Under the basic assumptions of g-expectations defined in Chen and Wang (2000), we establish the one-to-one correspondence between generators of backward stochastic differential equations (BSDEs for short) and the convexity (resp. conditional convexity, Ft-convexity) of g-expectations, respectively. We also obtain the relationship between generators of BSDEs and the sublinearity (resp. conditional sublinearity, Ft-sublinearity) of g-expectations, respectively. Moreover, we provide the reasonable assumptions on generators of BSDEs for the further study on dynamic risk measures by applying the theory of g-expectations.

Keywords: Convexity; Sublinearity; Backward stochastic differential equation; g-expectation; Dynamic risk measure (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109569

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