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A necessary and sufficient condition for probability measures dominated by g-expectation

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  • Jiang, Long

Abstract

We prove that if the generator g of a g-expectation is independent of y, then a probability measure Q is dominated by if and only if Q can be generated by the Girsanov transformation via a controlled process; furthermore, we prove that equals the supremum of its dominated mathematical expectations if and only if g is sublinear with respect to z.

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  • Jiang, Long, 2009. "A necessary and sufficient condition for probability measures dominated by g-expectation," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 196-201, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:2:p:196-201
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    References listed on IDEAS

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    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    2. 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.
    3. Jiang, Long, 2005. "Representation theorems for generators of backward stochastic differential equations and their applications," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1883-1903, December.
    4. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    5. Jiang, Long, 2006. "A note on g-expectation with comonotonic additivity," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1895-1903, November.
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    Cited by:

    1. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    2. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2022. "Convexity and sublinearity of g-expectations," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Ju Hong Kim, 2021. "The relations of Choquet Integral and G-Expectation," Papers 2102.10213, arXiv.org.

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