The prices of two stocks are governed by the following:
dX(t)/ X(t) = 0.05dt + 0.3dZ(t)
dY(t)/Y (t) = 0.04dt + 0.25dZ(t) where Z(t) is a standard Brownian motion.
Additionally, you know that the current stock prices are X(0) = 24 and Y (0) = 48. You wish to construct a risk-free portfolio that consists of 100 shares of X, N shares of Y , and investing B dollars at the risk-free rate. The cost of the portfolio should be 0. (a) N =?