3. Suppose a decision-maker has absolute local risk aversion r(f).

(a) Show that the risk of gain or loss of h with equal probability (±h, each with proba2 bility 1 ), is equivalent, asymptotically as h → 0, to the sure loss of h r(f). 2 2

(b) Show that the gain of ±h with respective probabilities (1 ± d)/2 is indifferent to hr

(f) you, asymptotically as h → 0, if d = . 2 ph(1 qh) gain r

(f)

(c) The price of a h with probability p is − · , where q = 1 − p.