Non-Markovian solvability of interacting quadratic BSDEs

Determine whether non-Markovian backward stochastic differential equations with interacting quadratic drivers admit solutions, including global well-posedness and uniqueness beyond the parameter regimes addressed by existing results.

Background

The paper studies a two-parameter family of quadratic backward stochastic differential equation systems whose components interact through the terms involving the sum of the control variables. It is motivated by a path-dependent two-player stochastic game and establishes generic well-posedness with respect to the terminal datum, rather than resolving solvability for every bounded terminal datum in the full non-Markovian setting.

The authors identify this broader non-Markovian solvability issue as an open question raised by Jackson. The paper provides partial progress through residual-set well-posedness, arbitrary solvability for two-valued terminal data, and a reduction of universal bounded solvability to three-valued terminal data, but it does not establish universal solvability for all bounded terminal data for arbitrary positive parameters.