Consider a complete one-period financial model, with a stock initially valued at So = 100, and = a risk-free bond has maturity of one year, with interest rate equal to r = 0.05, and at time 1, the stock has 3 possible outcomes (Si(wi), Si(wa), S(W3)) = (120, 100, 80), and = (2) 31 in the physical (real) world, it has been observed that each out- come occurs with equal probability , and a call on S time 1 with strike K = 100 costs 10 at time 0, and an investor has utility function U(X) = ln (X), and the investor wishes to maximize expected utility of wealth at time 1, under the physical measure, given an initial Xo = 100 to invest. Compute the optimal final value 1(w) for w=w1,w2 and w3 for this investor. (50 pts) = Consider a complete one-period financial model, with a stock initially valued at So = 100, and = a risk-free bond has maturity of one year, with interest rate equal to r = 0.05, and at time 1, the stock has 3 possible outcomes (Si(wi), Si(wa), S(W3)) = (120, 100, 80), and = (2) 31 in the physical (real) world, it has been observed that each out- come occurs with equal probability , and a call on S time 1 with strike K = 100 costs 10 at time 0, and an investor has utility function U(X) = ln (X), and the investor wishes to maximize expected utility of wealth at time 1, under the physical measure, given an initial Xo = 100 to invest. Compute the optimal final value 1(w) for w=w1,w2 and w3 for this investor. (50 pts) =