Let u(w), w 0, be a utility function of a risk averse insurer.

2. (a) Let who), to 2 0, be a utility function of a risk averse insurer. (i) Explain the non-satiation and the risk aversion property. (ii) Let u('w) = inn, 5 > 0. The insurer effects a proportional reinsurance with proportion a, 0 S a, g 1, against the random loss X. The distribution of X is estimated to be IP(X = 0) = p and iP(X = 1) = 1 p, with 0 S p S 1. Find the minimum premium P" that the insurer charges for such policy