When integrating the r(u) from t to T, i cannot work out how to deal with the item with double integration. In the exam report answer for this part, i don't get the same results for the third item integration which involves both deterministic and stochastic integral. I tried to integrate the third item with respect to u from t to u OR from t to T, either way, I can't get the same answer as the exam report. Could anyone please explain how exactly this double integration should be dealt with as i get confused by switching between different limits ? Please see the attached screenshot for the specific item i am asking.
In the double integral, the outer integral is with respect to the variable u. This outer integral has limits t and T. So t<u<T. The inner integral is with respect to the variable s. This has limits t and u. So t<s<u. Putting these inequalities together we have t<s<u<T. To switch the order of integration, we choose the "other" inequalities implied by this, ie s<u<T and t<s<T. So we now have the inner integration with respect to the variable u between the limits of s and T, and the outer integral with respect to the variable s between the limits of t and T. The inner integral has been carried out already in the ringed part of the solution shown.
