3. Let (Bt) denote a Brownian motion under the real-world measure with Bo = 0. Consider the Black-Scholes model for the stock price, dSt = 25+ dt + 45 dBt, So = 1, and the savings account is given by Bt = 1 for all t. = (a) Write down the condition for a portfolio in this model to be self-financing. Consider the portfolio given by at = -t (units of the stock) and by St Sydu (units of the savings account), determine with proof whether this portfolio is self-financing. 1 (b) State the Girsanov theorem. Using it, or otherwise, derive the expression (not the stochastic differential) for St, in terms of a Brownian motion under the equivalent martingale measure (EMM). (c) Denote by Ct the price at time t