2. Tom is the representative of a financial company, which can invest in a financial market, where 1. one can borrow and lend money for any period of time according to the riskless interest rate 0.0296. 2. one can buy or sell a forward contract for delivery of a stock at time N1 at a forward price F 150. 3. the price of the stock at time N 1 takes on a probability space (S2 F, P- P(wi) 0.3, P(w2) 0.7), the following values: S(wi130, S(2 180 A client of the company wants to invest Xo 100000. The utility function of the client equals U(x) In if > 0 and equals -oo if x 0. The client wi buy from Tom any derivative product, which gives the same expected utility as in the case of investment into a money market (saving) account with riskless rate r = 0.0296, Tom wants to maximize the profit of the financial company. Describe the payment function V of the derivative contract Tom will sell to the client. What profit will Tom make at time 0? 2. Tom is the representative of a financial company, which can invest in a financial market, where 1. one can borrow and lend money for any period of time according to the riskless interest rate 0.0296. 2. one can buy or sell a forward contract for delivery of a stock at time N1 at a forward price F 150. 3. the price of the stock at time N 1 takes on a probability space (S2 F, P- P(wi) 0.3, P(w2) 0.7), the following values: S(wi130, S(2 180 A client of the company wants to invest Xo 100000. The utility function of the client equals U(x) In if > 0 and equals -oo if x 0. The client wi buy from Tom any derivative product, which gives the same expected utility as in the case of investment into a money market (saving) account with riskless rate r = 0.0296, Tom wants to maximize the profit of the financial company. Describe the payment function V of the derivative contract Tom will sell to the client. What profit will Tom make at time 0