Consider a security market that contains one bond with price Pt and one stock with price St. Their dynamics are described by: [dPt = rP dt, t 0, Po = P, d St So = x. = Stdt + o StdWt, t 0, Suppose that an agent sells an European option on the stock St at price Y, 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 option based on the portfolio above. b) Using the Feynman-Kac formula, find the associated PDE. Consider a security market that contains one bond with price Pt and one stock with price St. Their dynamics are described by: [dPt = rP dt, t 0, Po = P, d St So = x. = Stdt + o StdWt, t 0, Suppose that an agent sells an European option on the stock St at price Y, 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 option based on the portfolio above. b) Using the Feynman-Kac formula, find the associated PDE