Consider a risky asset with following prices and assume that

Consider a risky asset with following prices and assume that we can invest money risk free at a rate r_1 = 3% and borrow money risk free at r = 5% The aim for the investor is to maximize the expected utility of terminal wealth E(u(V_x(1))) for an investment of W=1000. What is the optimial strategy and the optimal expected utility for the utility function: In (x) ?

Solution

optimal strategy will be

120 * 0.4 + 100 * 0.4 + 90 *0.2

106