1. The price of a US stock and the exchange rate Dollar/Euro are given by, with W having correlation p with W, dS(t)/S(t) = dt + odW(t) dQ(t)/Q(t) = Bdt + ddW(t) (i) Find the Brownian motions W and W such that the discounted dollar value of the euro bank account e-rtQ(t)erft is a martingale, and the discounted dollar value of the domestic stock e-t S(t) is also a martingale under the corresponding probability P*, where r and rf are the US and the Euro risk-free interest rates, respectively. (ii) Find the domestic price of the payoff of C(T) = log(Q(T)S (T)) dollars. 1. The price of a US stock and the exchange rate Dollar/Euro are given by, with W having correlation p with W, dS(t)/S(t) = dt + odW(t) dQ(t)/Q(t) = Bdt + ddW(t) (i) Find the Brownian motions W and W such that the discounted dollar value of the euro bank account e-rtQ(t)erft is a martingale, and the discounted dollar value of the domestic stock e-t S(t) is also a martingale under the corresponding probability P*, where r and rf are the US and the Euro risk-free interest rates, respectively. (ii) Find the domestic price of the payoff of C(T) = log(Q(T)S (T)) dollars