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Anticipated backward stochastic differential equations with quadratic growth: Multidimensional results

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  • Hu, Ying
  • Li, Feng
  • Wen, Jiaqiang

Abstract

In this paper, we study the solvability of multidimensional anticipated backward stochastic differential equations with quadratic growth. We establish three new results concerning both local and global solutions. More precisely, for the local solution with bounded terminal values, the generator f(t,Yt,Zt,Yt+δt,Zt+ζt) is of general growth in Yt and Yt+δt. For the global solution with bounded terminal values, the generator f(t,Yt,Zt,Yt+δt,Zt+ζt) is of skew sub-quadratic but is also “strictly and diagonally” quadratic growth in Zt. For the global solution with unbounded terminal values, the generator f(t,Yt,Zt,Yt+δt) is of diagonal quadratic growth in Zt in the first case; the generator f(t,Zt)+E[g(t,Yt,Zt,Yt+δt,Zt+ζt)] is of diagonal quadratic growth in Zt and linear growth in Zt+ζt in the second case.

Suggested Citation

  • Hu, Ying & Li, Feng & Wen, Jiaqiang, 2026. "Anticipated backward stochastic differential equations with quadratic growth: Multidimensional results," Stochastic Processes and their Applications, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:spapps:v:198:y:2026:i:c:s0304414926000736
    DOI: 10.1016/j.spa.2026.104941
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    References listed on IDEAS

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