Consider an individual who will be retiring in two years, i.e., at time + 2. His savings are invested in a mutual fund. Every year, the value of his portfolio increases by with probability and otherwise decreases by , where = . The individual's preferences can be represented by Prospect Theory. Specifically, his value function for gains and losses relative to the reference point (the value of the savings at time ) is

(x) = x, for 0 ; for <0

where > 1. Furthermore, his probability weighting function is () = , and his time discount factor is = 0.5. The individual wants to maximize his utility from wealth at retirement. If, at the end of the first year (time + 1), the individual observes that his investments have gone down by , does he optimally choose to stay invested in the fund or not? Discuss. Also discuss how your answer would change if

(x) = xfor 0 () for < 0

for > 0