1 An insurer with net worth 100 has accepted and collected t

1. An insurer with net worth 100 has accepted (and collected the premium for) a risk X with the following probability distribution: Pr(X = 0) = Pr(X = 51) =1/2 : What is the maximum amount G it should pay another insurer to accept 100% of this loss? Assume the first insurer\'s utility function of wealth is u(w) = log w. 2. An insurer, with wealth 650 and the same utility function u(w) = log w, is considering accepting the above risk. What is the minimum amount H this insurer would accept as premium to cover 100% of the loss?

Solution

a) Maximum amount Gis such that:

u(100 +/- X) = u(100+/- G)

(1/2) log(100 +/- 0) + (1/2)log(51 +/-0) = log(100+/- G)

solve : log(10*51/2) = log(100+/-G)

G = 30

b) minium amount of H :

u(650 +/-H +/- X) = u(650)

(1/2)log(650 +H +/- 0) + (1/2)log(650 +H +/- 51) = log(650)

on solving above equation we get H = 26