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 .