Before revision:  The control  process of the BSDE steers the system into a random liabilitydepending on a market external uncertainty and this way describes the optimal derivative hedge of the liability by investment in a capital market the dynamics of which is described by the forward component.
After revision:  The control process of the BSDE steers the system into a random liabilitydepending on a market external uncertainty and this way describes the optimal derivative hedge of the liability by investment in the capital market the dynamics of which is described by the forward component.