Let a stock price be a geometric Brownian motion dS(t) = oS(t)dt + S(t)dW(t) Let r denote the interest rate. We define the market price of risk to be -r and the state price density process to be a. Show that d(t)C(t)dt C(t)dW (t) b. Let X denote the value of an investors portfolio when he uses a portfolio process (t). That is we have dx(t)-rx(t)dt + (t)(a-r)S(t)dt + (t)oS(t)dW(t). Show that (t)x(t) is a martingale. d (E(t)x(t))) has no dt term). (Hint Show that the differential Let a stock price be a geometric Brownian motion dS(t) = oS(t)dt + S(t)dW(t) Let r denote the interest rate. We define the market price of risk to be -r and the state price density process to be a. Show that d(t)C(t)dt C(t)dW (t) b. Let X denote the value of an investors portfolio when he uses a portfolio process (t). That is we have dx(t)-rx(t)dt + (t)(a-r)S(t)dt + (t)oS(t)dW(t). Show that (t)x(t) is a martingale. d (E(t)x(t))) has no dt term). (Hint Show that the differential