In the setting of Sect. 6.4, consider a fixed \(t \in\{0,1, \ldots, T-2\}\) and suppose at date \(t\) it is possible to trade a zero-coupon bond with maturity \(t+1\) having price \(B(t, t+1)\) and a zero-coupon bond with maturity \(t+2\) having price \(B(t, t+2)\). Suppose furthermore that at the future date \(t+1\) it will be possible to trade a zero-coupon bond with maturity \(t+2\) for the price \(B(t+1, t+2)\). Let \(\mathbb{P}^{*}\) be a risk neutral probability measure for the economy. Prove that

\[B(t, t+2)=B(t, t+1) \mathbb{E}^{*}\left[B(t+1, t+2) \mid \mathscr{F}_{t}\right] .\]