2005/05/01 by Zengjing Chen, Tao Chen, Matt Davison · 3 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #msc:60G48 #msc:60H10
paper · pdf · doi:10.1214/009117904000001053
published as Annals of Probability 2005, Vol. 33, No. 3, 1179-1199 · Published at http://dx.doi.org/10.1214/009117904000001053 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/05/01 · arxiv created 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.