Consider a risk neutral representative agent economy under the assumption of rational expectations, with a risky security paying the dividend stream \(\left(d_{t}\right)_{t \in \mathbb{N}}\), which is supposed to follow a first order autoregressive process of the form (9.63). Assume furthermore that the dividend process \(\left(d_{t}\right)_{t \in \mathbb{N}}\) is predictable, meaning that the random variable \(d_{t+1}\) is \(\mathscr{F}_{t}\)-measurable, for every \(t \in \mathbb{N}\). Starting from equation (9.62), show that the rational expectations solution for the price process \(\left(s_{t}\right)_{t \in \mathbb{N}}\) of the risky security is given by (9.64).