Risk Pooling Class Problem and Solution

PDF’s of today’s class problem and solutions are available here:

Note also that the probability of a loss exceeding $1,500 when n =1 (i.e., when there is no risk pooling) is:

N\left( {\displaystyle\frac{{1,500 - E({L_i})}}{{{\sigma _{{L_i}}}}}} \right) = N\left( {\displaystyle\frac{{1,500 - 1,000)}}{{1,000}}} \right) = N(.5) = 30.85{\rm{\% }}.

This problem showcases the tremendous advantage afforded to consumers from the pooling of risk, by reducing the probability of a large loss by almost 60% when risks are iid and n =5 (question 1), and by reducing the probability of a large loss by more than 80% when risks are iid and n =10 (question 2).  However, the introduction of positive correlation in question 3 significantly reduces the efficacy of risk pooling, since for n =10 and {\rho _{12}} = .1, there is a 12.57% probability that the loss on an average policy will exceed $1,500.

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