## The Annals of Probability

### Choquet expectation and Peng’s g-expectation

#### Abstract

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

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

Dates
First available in Project Euclid: 6 May 2005

http://projecteuclid.org/euclid.aop/1115386723

Digital Object Identifier
doi:10.1214/009117904000001053

Mathematical Reviews number (MathSciNet)
MR2135317

Zentralblatt MATH identifier
1066.60054

#### Citation

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. http://projecteuclid.org/euclid.aop/1115386723.

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