By the comparison theorem, a series of properties of the backward-forward differential utility process is gotten, such as time consistence, monotonicity with respect to the terminal value, monotonicity with respect to the consumption and concavity.

• 运用比较定理，还证明了正倒向随机微分效用过程的时间一致性、终值单调性、消费单调性和凹性等有关性质。