The Annals of Probability

Choquet expectation and Peng’s g-expectation

Zengjing Chen, Tao Chen, and Matt Davison

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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.

Article information

Ann. Probab. Volume 33, Number 3 (2005), 1179-1199.

First available in Project Euclid: 6 May 2005

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60G48: Generalizations of martingales

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


Chen, Zengjing; Chen, Tao; Davison, Matt. Choquet expectation and Peng’s g -expectation. Ann. Probab. 33 (2005), no. 3, 1179--1199. doi:10.1214/009117904000001053.

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