Hi guys, I managed to do this question except for the red part, please guys help me in this because I really dont have a clue as to what does this represent. Q: An investor has wealth X and invests a proportion (alpha) in a risky asset that will increase in value by y% (so that an investment of 1 would increase to 1+y) with probability p and fall to zero with probability 1 − p. The amount not invested in the risky asset will neither increase nor decrease in value. (a) If the investor has a utility function U(w) = ln(w) then show that expected utility is maximimized by maximizing lnX + p ln(1 + alpha*y) + (1 − p) ln(1 − alpha) (b) Hence show that expected utility is maximized when alpha = {yp- (1-p)}/{y} What does the numerator represent?
W is the random variable wealth W= x*{(1-alpha) +alpha*(1+y)} with probability p W=x*(1-alpha) with probability (1-p) E[W] = x*{1 + [yp -(1-p)]*alpha} %change = (final-initial)/initial E[%change]=(E[W]-x)/x =[yp -(1-p)]*alpha so [yp -(1-p)] is the expected % change in wealth per alpha what this means is anyones guess
