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Mean-field type quadratic BSDEs

  • *Corresponding author: Ying Hu

    *Corresponding author: Ying Hu 
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  • 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.

    Mathematics Subject Classification: Primary: 60H10.

    Citation:

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    [8] R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games With Applications, I. Mean Field Fbsdes, Control, and Games, Probability Theory and Stochastic Modelling, 83 (2018), Springer, Cham.
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