Article Dans Une Revue Stochastic Processes and their Applications Année : 2026

Anticipated Backward Stochastic Differential Equations with Quadratic Growth: Multidimensional Results

Ying Hu
  • Fonction : Auteur
  • PersonId : 829971
  • IdHAL : ying-hu
Feng Li
  • Fonction : Auteur
Jiaqiang Wen

Résumé

This paper is devoted to the general solvability of anticipated backward stochastic differential equations with quadratic growth by relaxing the assumptions made by Hu, Li, and Wen [21, Journal of Differential Equations, 270 (2021), 1298-1311] from the one-dimensional case with bounded terminal values to the multi-dimensional situation with bounded/unbounded terminal values. Three new results regarding the existence and uniqueness of local and global solutions are established. More precisely, for the local solution with bounded terminal values, the generator f (t, Y t , Z t , Y t+δt , Z t+ζt ) is of general growth with respect to Y t and Y t+δt . For the global solution with bounded terminal values, the generator f (t, Y t , Z t , Y t+δt , Z t+ζt ) is of skew sub-quadratic but also "strictly and diagonally" quadratic growth in Z t . For the global solution with unbounded terminal values, the generator f (t, Y t , Z t , Y t+δt ) is of diagonal quadratic growth in Z t in the first case; and in the second case, the generator f (t, Z t ) + E[g(t, Y t , Z t , Y t+δt , Z t+ζt )] is of diagonal quadratic growth in Z t and linear growth in Z t+ζt .

Fichier principal
Vignette du fichier
2503.20255v2.pdf (451.77 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05561891 , version 1 (21-03-2026)

Licence

Identifiants

Citer

Ying Hu, Feng Li, Jiaqiang Wen. Anticipated Backward Stochastic Differential Equations with Quadratic Growth: Multidimensional Results. Stochastic Processes and their Applications, 2026, pp.104941. ⟨10.1016/j.spa.2026.104941⟩. ⟨hal-05561891⟩
113 Consultations
59 Téléchargements

Altmetric

Partager

  • More