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 Electronic Communications in Probability > Vol. 5 (2000) > Paper 13 open journal systems 


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

Philippe Briand, Université Rennes 1
François Coquet, Université Rennes 1
Ying Hu, Université Rennes 1
Jean Mémin, Université Rennes 1
Shige Peng, Shandong University


Abstract
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 $g_1equiv g_2$. 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].


Full text: PDF

Pages: 101-117

Published on: May 23, 2000


Bibliography
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  8. S. Peng, Backward SDE and related g-expectation, in Backward stochastic differential equations, 141--159, Pitman res. Notes Math. Ser., 364, Longman, Harlow, 1997. Math. Review number not vailable.
  9. S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob--Meyer's type, Probab. Theory Related Fields 113 (1999), no. 4, 473--499. Math. Review 1717527.
  10. F. Pradeilles, Wavefront propagation for reaction-diffusion systems and backward SDEs, Ann. Probab. 26 (1998), no. 4, 1575--1613. Math. Review 2000e:35103.
  11. R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970. Math. Review 43#445.
















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Electronic Communications in Probability. ISSN: 1083-589X