Mean-field type Quadratic BSDEs
Probability
2017-08-30 v1
Abstract
In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean, the general case can be treated by a fixed point argument.
Cite
@article{arxiv.1708.08784,
title = {Mean-field type Quadratic BSDEs},
author = {Hélène Hibon and Ying Hu and Shanjian Tang},
journal= {arXiv preprint arXiv:1708.08784},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1408.4579