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Jensen’s inequality for g-expectations in general filtration spaces

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  • Song, Wenjie
  • Wu, Panyu
  • Zhang, Guodong

Abstract

In this paper, we investigate the properties of BSDEs in general filtration spaces based on the transposition solutions. We obtain a result that Jensen’s inequality holds under the g-expectation and conditional g-expectation in general filtration spaces if and only if g is independent of y and super-homogeneous in z.

Suggested Citation

  • Song, Wenjie & Wu, Panyu & Zhang, Guodong, 2021. "Jensen’s inequality for g-expectations in general filtration spaces," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302613
    DOI: 10.1016/j.spl.2020.108958
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    References listed on IDEAS

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    1. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    2. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Du, Kai & Zhang, Qi, 2013. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1616-1637.
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