ActivePortfolioManagement/P179/v(t)的期望值是1.md

由定义：

[ v(s,T) = \frac{\pi^*(s,T)}{\pi(s,T)} ] 因为比较两个求和式可得：

[ \pi(s,T) v(s,T) = \pi^*(s,T) ] 所以：

[ v(s,T) = \frac{\pi^*(s,T)}{\pi(s,T)} ] 于是：

[ \mathbb{E}\pi[v(s,T)] = \sum{s} \pi(s,T) \cdot \frac{\pi^(s,T)}{\pi(s,T)} = \sum_{s} \pi^(s,T) = 1 ]