Electronic Communications in Probability

A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation

Philippe Briand, François Coquet, Ying Hu, Jean Mémin, and Shige Peng

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In [1], Z. Chen proved that, if for each terminal condition $\xi$, the solution of the BSDE associated to the standard parameter $(\xi, g_1)$ is equal at time $t=0$ to the solution of the BSDE associated to $(\xi, g_2)$ then we must have $g_1\equiv g_2$. This result yields a natural question: what happens in the case of an inequality in place of an equality? In this paper, we try to investigate this question and we prove some properties of ``$g$-expectation'', notion introduced by S. Peng in [8].

Article information

Electron. Commun. Probab., Volume 5 (2000), paper no. 13, 101-117.

Accepted: 23 May 2000
First available in Project Euclid: 2 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Backward stochastic differential equations comparison theorem

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Briand, Philippe; Coquet, François; Hu, Ying; Mémin, Jean; Peng, Shige. A Converse Comparison Theorem for BSDEs and Related Properties of g-Expectation. Electron. Commun. Probab. 5 (2000), paper no. 13, 101--117. doi:10.1214/ECP.v5-1025. https://projecteuclid.org/euclid.ecp/1456943506

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