Betty Bad and Gary Good have the following expected claims distributions: Betty Bad Gary Good Loss $10,000 $5,000 $1,000 Probability of Loss $ .10 .20 .30 $ 0 .40 $10,000 .05 $5,000 .10 $1,000 .15 0 .70 What are the expected claims costs for Betty Bad and Gary Good respectively? What is the expected average claims cost per policy for a pool in which 50% of the participants have claims distributions identical the Betty Bad and 50% have claims distributions identical to Gary Good. If insurers cannot distinguish the Goods from the Bads, what is the potential problem with charging everyone a premium equal to the expected average claims costs?

Practical Management Science
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Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Betty Bad and Gary Good have the following expected claims distributions:
Betty Bad
Gary Good
Loss
Probability
of Loss
.10
.20
.30
$ 0
.40
$10,000 .05
$5,000 .10
$1,000 15
0 .70
$10,000
$5,000
$1,000
$
What are the expected claims costs for Betty Bad and Gary Good respectively?
What is the expected average claims cost per policy for a pool in which 50% of the
participants have claims distributions identical the Betty Bad and 50% have claims
distributions identical to Gary Good.
i) If insurers cannot distinguish the Goods from the Bads, what is the potential problem
with charging everyone a premium equal to the expected average claims costs?
Transcribed Image Text:Betty Bad and Gary Good have the following expected claims distributions: Betty Bad Gary Good Loss Probability of Loss .10 .20 .30 $ 0 .40 $10,000 .05 $5,000 .10 $1,000 15 0 .70 $10,000 $5,000 $1,000 $ What are the expected claims costs for Betty Bad and Gary Good respectively? What is the expected average claims cost per policy for a pool in which 50% of the participants have claims distributions identical the Betty Bad and 50% have claims distributions identical to Gary Good. i) If insurers cannot distinguish the Goods from the Bads, what is the potential problem with charging everyone a premium equal to the expected average claims costs?
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