Exercise 4

A decision-maker D-M possessing assets w>10 mln is exposed to risk X

Probability of loss	Severity of loss
0,90	0
0,10	2 mln

D-M behaves in line with the expected utility theory and evaluates his financial position according to utility function uw=b2-b-w2 , where b is a positive constant, b3w .

1. identify the attitude toward risk of D-M,
2. it is known, that D-M has bought at premium P an insurance policy to fully protect assets w from risk X. Analyse the correctness of the following statements:

(b1) D-M would also pay P to buy the same policy if he were possessing 0,5w

(b2) D-M would also pay P to buy the same policy if he were possessing 2w.

{Hint: Start with analysis of the utility function u(w). You should demonstate that u(w)>0 ; u(w)<0; rw=1b-w and r'w=1(b-w)2>0 and conclude that D-M exhibits the increasing risk aversion when his assets grow. Thus (b2) is true since a possession of 2w may only increase his risk aversion, ceteris paribus. Contrarry to that by asset of 0,5w his risk aversion should decrease and this may change his willingness to buy insurance.}