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Lecture 07 - Risk Pooling II

# Lecture 07 - Risk Pooling II - Effects of Risk Pooling A...

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Effects of Risk Pooling A: Each Person Alone Outcome Probability \$0 0.95 \$10,000 0.05 B: Pooling with 2 People Outcome Probability \$0 0.9025 \$5,000 0.095 \$10,000 0.0025

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Effect of Risk Pooling Effect on Expected Loss w/o pooling, each faces expected loss = \$500 with pooling, each faces expected loss = \$500 Effect on Variance of Loss w/o pooling, loss variance = \$4,750,000 with pooling, loss variance = \$2,375,000
Risk Pooling with 4 People Pooling Arrangement between 4 people: Outcome Probability \$10,000 0.000006 \$7,500 0.000475 Loss = \$5,000 0.014 \$2,500 0.171 \$00.815 Expected Loss = \$500 Variance = \$1,187,500

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Mathematics of Risk Pooling If losses across individuals are uncorrelated (independent) E(Average Loss) = E(Individual Loss) Var(Average Loss) = Var(Individual Loss) N where N = number in insurance pool
Average Losses as the Sample Mean “Average loss per person” in a pooling arrangement is the sample mean of losses. Average Loss = Sum of individual losses = X Number in Pool The sample mean has a probability distribution that tends toward the normal distribution centered around the true mean. The insurance pool faces risk but not as much risk as each individual alone. Average losses become much more predictable as more observations are added to the sample

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When N Grows Large
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Lecture 07 - Risk Pooling II - Effects of Risk Pooling A...

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