Abstract
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9].
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References
Peng, S., Backward stochastic differential equations and related g-expectation, Backward Stochastic Dif- ferential Equations, N. El. Karoui and L. Mazliak (eds.), Pitman Research Notes in Math. Series, No. 364, Longman Harlow, 1997, 141–159.
Chen, Z. and Epstein, L., Ambiguity, risk and asset returns in continuous time, Econometrica, 70, 2002, 1403–1443.
Rosazza, G. E., Some examples of risk measure via g-expectations, Working Paper, Università di Milano Bicocca, Italy, 2004.
Briand, P., Coquet, F., Hu, Y., Mémin, J. and Peng, S., A converse comparison theorem for BSDEs and related properties of g-expectation, Electron. Comm. Probab., 5, 2000, 101–117.
Coquet, F., Hu, Y., Mémin, J. and Peng, S., A general converse comparison theorem for backward stochas- tic differential equations, C. R. Acad. Sci. Paris, Série I, 333(7), 2001, 577–581.
Coquet, F., Hu, Y., Mémin, J. and Peng, S., Filtration consistent nonlinear expectations and related g-expectation, Probab. Theory and Related Fields, 123(1), 2002, 1–27.
Chen, Z., Kulperger, R. and Jiang, L., Jensen’s inequality for g-expectation: Part 1, C. R. Acad. Sci. Paris, Série I, 337(11), 2003, 725–730.
Chen, Z., Kulperger, R. and Jiang, L., Jensen’s inequality for g-expectation: Part 2, C. R. Acad. Sci. Paris, Série I, 337(12), 2003, 797–800.
Jiang, L. and Chen, Z., On Jensen’s inequality for g-expectation, Chin. Ann. Math., 25B(3), 2004, 401–412.
Jiang, L., A property of g-expectation, Acta Math. Sinica, English Series, 20(5), 2004, 769–778.
Pardoux, E. and Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Let., 14, 1990, 55–61.
Jiang, L., Nonlinear Expectation—g-Expectation Theory and Its Applications in Finance, Doctoral Dis- sertation, Shandong University, China, 2005.
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*Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.
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Jiang, L. Jensen’s Inequality for Backward Stochastic Differential Equations*. Chin. Ann. Math. Ser. B 27, 553–564 (2006). https://doi.org/10.1007/s11401-005-0077-0
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DOI: https://doi.org/10.1007/s11401-005-0077-0
Keywords
- Backward stochastic differential equation
- g-Expectation
- Jensen’s inequality for g-expectation
- Jensen’s inequality for BSDEs