Mean-field type Quadratic BSDEs

Hélène Hibon; Ying Hu; Shanjian Tang

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arXiv · 1708.08784

Mean-field type Quadratic BSDEs

Hélène Hibon·Ying Hu·Shanjian Tang

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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.

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BibTeX RIS

Hélène Hibon, Ying Hu, Shanjian Tang. 2017-08-28. Mean-field type Quadratic BSDEs. https://arxiv.org/abs/1708.08784

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