AUTOMOBILE INSURANCE: MORAL HAZARD AND ADVERSE SELECTION
Data from an automobile insurance company show that claims frequency and size are affected by what type of insurance is chosen by an individual? The data are from an Israeli insurer for the years 1994-1999. Table provides relevant data. Model the claims frequency using a Poisson distribution (to allow for more than one claim per policy holder) and use a Lognormal distribution for the size of claims (with the mean given in Table and standard deviation equal to the mean). Assume that 1,000 drivers are insured by the policies, in the proportions indicated in Table Also assume that there is no correlation between policy types. Build a simulation model to
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Table - Insurance Policy Types
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Policy Type
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Average Premium
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Deductible
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Claim Frequency
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Average Damage/Claim
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Percentage Choosing
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Regular
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2,800
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1,400
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21.33%
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11,433
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76.72
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Low deductible
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3,640
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840
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27.76%
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10,233
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21.96
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High deductible
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1,960
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2,520
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15.05%
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13,600
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0.74
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Very High deductible
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1,920
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3,640
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11.37%
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10,750
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0.6
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a. Estimate the contribution margin (revenue minus direct costs from claims-that is, what is left to cover overhead costs and profits) per insured driver-for each policy type and for the total of all drivers insured by this company.
b. See whether the differences in premiums appear to match the differences in expected costs across policies.
c. Determine the overall probability that this company will have a positive contribution. What level of contribution do you estimate there is a 95% likelihood of achieving or exceeding?