A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE
arXiv:1301.4370 · doi:10.1142/S0219493713500056
Abstract
In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.
accepted for publication