I am trying to see if the following statement is true or not and I would really appreciate your help.
The statement is as follows:
$\forall $ Tradable Asset $V(t)$, $$ E[\frac{P(t,T_{i})P(T_{i},T_{i+1})}{P(t,T_{i+1})}V(T_i)|F_t] = E[V(T_i)|F_t]$$ Where the expectency is taken under any probability measure (not necessarily Risk neutral) although a solution with the Risk neutral measure is also more than welcome.
My intuition is that $P(t,T_{i})P(T_{i},T_{i+1}) \approx P(t,T_{i+1})$ especially under expectencies.
PS: $T(t,T_i)$ is the $T_i$ zero coupon bond price at time t.
Many thanks