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May 2005 Choquet expectation and Peng’s g-expectation
Zengjing Chen, Tao Chen, Matt Davison
Ann. Probab. 33(3): 1179-1199 (May 2005). DOI: 10.1214/009117904000001053


In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng’s g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficient condition which proves that the only expectation which lies in both classes is the traditional linear expectation. This settles another open question about whether Choquet expectation may be used to obtain Monte Carlo-like solution of nonlinear PDE: It cannot, except for some very special cases.


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Zengjing Chen. Tao Chen. Matt Davison. "Choquet expectation and Peng’s g-expectation." Ann. Probab. 33 (3) 1179 - 1199, May 2005.


Published: May 2005
First available in Project Euclid: 6 May 2005

zbMATH: 1066.60054
MathSciNet: MR2135317
Digital Object Identifier: 10.1214/009117904000001053

Primary: 60G48 , 60H10

Keywords: Backward stochastic differential equation (BSDE) , Choquet-expectation , g-expectation , representation theorem of g-expectation

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 3 • May 2005
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