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 component of its solution. The latter is relevant in the context of securitization of random liabilities arising from exogenous risk, which are optimally hedged by investment in a given financial market with respect to exponential preferences. In a purely stochastic formulation, 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.