Consider a security market that contains one bond with price Pt and one stock with price St. Their dynamics are described by: (dPt = rPt dt, t 0, PO = p. (dSt = Stdt + oSt dWt, t 0, S0 = x. Suppose that an agent sells a European option on the stock St at price Yt and then invests it in the market. Assume that at each time the agent invests a portion of the amount Yt given by At into the stock, and the rest (Yt-At) into the bond. Now the agent has a portfolio based on the two securities. a) Derive the BSDE for pricing European options based on the portfolio above. b) Using the Feynman-Kac formula, find the associated PDE.