In the context of Proposition 6.8, suppose that, for all \(t=1, \ldots, T-1\), the \(\mathscr{F}_{t}\)-conditional distribution of the asset returns \(r_{t+1}^{n}, n=1, \ldots, N\), coincides with the unconditional distribution of \(r_{1}^{n}, n=1, \ldots, N\). Prove that the optimal portfolio process \(\left(w_{t}^{*}\right)_{t=1, \ldots, T}\) can be characterized as in equation (6.29), does not depend on time and that the process \(\left(a_{t}\right)_{t=0,1, \ldots, T}\) appearing in Proposition 6.8 reduces to a deterministic function of time.