Before revision:  In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability , and describes its optimal derivative hedge by investment in the capital market  the dynamics of which is given by the forward component .
After revision:  In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability and describes its optimal derivative hedge by investment in the capital market the dynamics of which is given by the forward component .