Abstract
The talk focuses on the general solvability of multi-dimensional non-Markovian backward stochastic differential equations (BSDEs) with interactively quadratic generators. Some general structures of the generator g are posited for both local and global existence and uniqueness results on BSDEs, which admit a general growth of the generator g in the state variable y, and a quadratic growth of the ith component g^i both in the jth row z^j of the state variable z for j≠i (by which we mean the “interactively quadratic" growth) and in the ith row z^i of z. We first establish an existence and uniqueness result on local bounded solutions and then several existence and uniqueness results on global bounded and unbounded solutions. They improve several existing works in the non-Markovian setting, and also incorporate some interesting examples, one of which is a partial answer to the problem posed in [Jackson,2023,SPA]. This ia a joint work with Shengjun Fan and Shanjian Tang.