Definition 2.3(DF process). If { ξ(t),tε[0,∞)} is a stochastic process, and 
ξ (t)εP(µ(t), σ2(t)t)
then { ξ (t),tε[0,∞)} is called a DF process.
Definition 2.4. Let a and b be non-negative constants, If a>0,b=0, we define:
Definition 2.5(DF structure). Let X be the value of an asset related to stock S(t)εP( µ(t), σ2(t)), if and T>t, Xs(t,T)εP(X, D[S(t)](T-t)), then we call Xs(t,T) the DF stochastic structure of X on
S(t). Xs(t,T) is called a DF structure of X for short.
When t=T, Xs(t,T)=X. So the actual meaning of the DF structure, Xs(t,T), is a stochastic value which is equal to that of an cash asset X in the future time T under-taking no discount of the interest rate.
Although the stock S(t) has certain connections with DF structure Xs(t,T) in variance, their stochastic movements may have no inevitable relation, so we have
Assumption 2.2. Let Xs(t,T) be the DF structure of X on S(t), thus Xs(t,T) and S(t) are independent of each other.
Prof. Feng Dai, Prof. Zifu Qin
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Summary: Index