Suppose that Kate and Anne enter into a pooling arrangement. Assume that both wo
ID: 3305135 • Letter: S
Question
Suppose that Kate and Anne enter into a pooling arrangement. Assume that both women have the following loss distributions and that losses are independent.
Loss ($)
Probability
50,000
0.005
20,000
0.010
10,000
0.020
0
0.965
A. Write out the possible outcomes and the probability of each outcome for Kate and Anne after they enter into a pooling arrangement. That is, write out the probability distribution for each of the women after they enter to pooling arrangement.
B. Calculate the expected loss to each person prior to and subsequent to entering into a pooling arrangement.
C. What happens to the standard deviation of the distribution of losses to each individual subsequent to the pooling arrangement? Support your answer. (HINT: You do not need to calculate standard deviations to answer this question.)
Loss ($)
Probability
50,000
0.005
20,000
0.010
10,000
0.020
0
0.965
Explanation / Answer
b) Expected cost summation of x*P(x) =650 remain same prior to pooling and after pooling.
c) subsequent to the pooling arrangement:
uncertainty reduces (variance decreases, losses become morepredictable, maximum probable loss declines)
distribution of costs becomes more symmetric (lessskewness)
Possible outcome Loss Cost paid by each( average Loss) Probability Kate had loss and Anne did not 50,000 25,000 0.005*0.995=0.004975 Kate had loss and Anne did not 20,000 10,000 0.01*0.99=0.0099 Kate had loss and Anne did not 10,000 5,000 0.02*0.98=0.0196 Neither Kate nor anne had loss 0 0 0.965*0.965=0.931 Anne had loss kate did not 50,000 25,000 0.005*0.995=0.004975 Anne had loss kate did not 20,000 10,000 0.01*0.99=0.0099 Anne had loss kate did not 10,000 5,000 0.02*0.98=0.0196 Both Anne and Kate had loss 100,000 50,000 0.005*0.005=0.000025 Both Anne and Kate had loss 40,000 20,000 0.01*0.01=0.0001 Both Anne and Kate had loss 20,000 10,000 0.02*0.02=0.0004Related Questions
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