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Article Dans Une Revue Numerical Algebra, Control and Optimization Année : 2023

Mean-field type Quadratic BSDEs

Hélène Hibon
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  • PersonId : 1006979
Ying Hu
  • Fonction : Auteur
  • PersonId : 829971
  • IdHAL : ying-hu
Shanjian Tang
  • Fonction : Auteur
  • PersonId : 968042

Résumé

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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Dates et versions

hal-01512453 , version 1 (23-04-2017)
hal-01512453 , version 2 (27-08-2017)

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Hélène Hibon, Ying Hu, Shanjian Tang. Mean-field type Quadratic BSDEs. Numerical Algebra, Control and Optimization, 2023, 13 (3-4), pp.392-412. ⟨10.3934/naco.2022009⟩. ⟨hal-01512453v2⟩
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