For the Black–Scholes economy described in Exercise 6, let N denote an EMM corresponding to the numeraire N = D + S. (i) Find the SDE satisfied by A N , N under the measure N. (ii) Use your working in...

For the Black–Scholes economy described in Exercise 6, let N denote an EMM corresponding to the numeraire N = D + S.

(i) Find the SDE satisfied by A^N, N under the measure N.

(ii) Use your working in (i) and Lemma 5.17 to show that

Where

Let
 be an
  predictable process bounded above and below by positive constants. Consider the Black–Scholes economy described in Exercise 6 but where now

(i) Find the SDE satisfied by

(ii) Show that there exists a unique
  corresponding to the numeraire S.

(iii) Find the solution to the SDE in (i) using Girsanov’s theorem.