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证明是前向布朗
定义和内容: 考虑一个经过过滤的概率空间,其中(Ω,F,{Ft}t∈[0,T],P)(Ω,F,{Ft}t∈[0,T],P)(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P) T>0T>0T > 0 P=P~P=P~\mathbb P = \tilde{\mathbb P} 这是风险中性的措施。 Ft=FWt=FW~tFt=FtW=FtW~\mathscr F_t = \mathscr F_t^{{W}} = \mathscr F_t^{\tilde{W}} 其中是标准的布朗运动。W=W~={Wt~}t∈[0,T]={Wt}t∈[0,T]W=W~={Wt~}t∈[0,T]={Wt}t∈[0,T]W = \tilde{W} = \{\tilde{W_t}\}_{t \in [0,T]} = \{{W_t}\}_{t \in [0,T]}P=P~P=P~\mathbb P=\tilde{\mathbb P} 考虑其中M={Mt}t∈[0,T]M={Mt}t∈[0,T]M = \{M_t\}_{t \in [0,T]} Mt:=exp(−∫t0rsds)P(0,t)Mt:=exp(−∫0trsds)P(0,t)M_t := \frac{\exp(-\int_0^t r_s ds)}{P(0,t)} …