Consider the Black-Scholes model. Namely, the stock price (St) is governed by the SDE dSt = μStdt + σStdBt, S0 = 1, where (Bt) is a Brownian motion under the real world probability measure P, and the value of the savings account is given by βt = ert. Let ˜Bt = Bt + (μ-2r)/σ t. (a) Justify the existence of a probability measure Q equivalent to P such that (˜Bt) is a Brownian motion under Q. (b) Show through calculation that (St/βt) is not a martingale under Q. (c) The Black-Scholes model is complete and possesses the EMM Q which turns ˆBt = Bt + (μ-r)/σ t into a Brownian motion. By solely appealing to completeness of the model, explain why (St/βt) could never have been a martingale under Q.