Choquet expectation and Peng's g-expectation

Details Choquet expectation and Peng's g-expectation Choquet expectation and Peng's g-expectation

2005-06-29

arxiv.org/abs/math/0506598v1

Annals of Probability 2005, Vol. 33, No. 3, 1179-1199

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000001053 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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