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Convexity and sublinearity of g-expectations

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  • Ji, Ronglin
  • Shi, Xuejun
  • Wang, Shijie
  • Zhou, Jinming

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.

Suggested Citation

  • Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2022. "Convexity and sublinearity of g-expectations," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001249
    DOI: 10.1016/j.spl.2022.109569
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    References listed on IDEAS

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    1. Bion-Nadal, Jocelyne, 2009. "Time consistent dynamic risk processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 633-654, February.
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