Before revision:  We start with the interpretation of the generator of a backward stochastic differential equation as an infinitesimal pricing rule or an instantaneous utility. With this interpretation the generator has an economic meaning and describes the subjective views of the investor concerning the expected change in the price or the utility. We give a motivation for considering non-Markovian generators of BSDEs which leads us to{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).
After revision:  We start with the interpretation of the generator of a backward stochastic differential equations with time-delayed generators of a moving average type. The classical and well-known framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (\frac{1{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).