Q.1. (PT and Risk Diversication) Recall the risk diversication question from the previous problem set where we showed that EU agents who derive utility from wealth will always diversify their portfolio: they will not invest in just one asset. Redo the problem by assuming that the agent is a Prospect Theory type. In particular, for simplicity, assume that there is no distortion of probabilities, and that the agent's current wealth w serves as the reference point. The utility from gains is u(9:) = J; for x Z 0 and the utility from losses is u(93) = A\\/|E| for 9: S 0 and some loss aversion parameter A > 1. As before, there are two assets, A and B, both of which (independently) return $100 with 0.75 probability and -$100 with 0.25 probability. Assume for simplicity that she is permitted to only hold fractions a and 1 oz of assets A and B respectively, where 0 S a 5 1. (As before, to simplify the calculations, we are forcing the agent to own a portfolio of assets, and she does not pay a price for Obtaining it). (i) Write down the agent's prOSpect theory utility correSponding to a: = 1. Next, write the corresponding utility for a generic (:2. (ii) Determine the shares a and 1 a of the assets that the agent buys. Does the agent diversify? Provide an intuition for your