Question

Q1: Suppose Joe and Leo both face the following individual loss distribution: Probability of Loss Amount of Loss 0.6 $0 0.3 $40 0.1 $80

A. Please calculate the expected loss and standard deviation of the expected loss faced by either Joe or Leo on an individual basis.

B. Suppose that Joe and Leo enter into a pooling-of-losses arrangement. Just state what will happen to the expected loss and variability of the expected loss as a result of the pooling arrangement (you don’t need to calculate)

Answer 1

A. Expected Loss= 0.6×0 + 0.3×40 + 0.1×80 = 20

Variance =( 0.6 × + 0.3 × + 0.1 × ) -

= 1120- 400

= 720

Standard deviation = = 26.83

B. In the case of pooling,the expected loss remains the same amongst the two but the variance reduces as the risk gets dispersed as people start sharing the risk.