Suppose a car insurance company divides claims from automobile accidents into fo

Question

Suppose a car insurance company divides claims from automobile accidents into four categories: trivial claims where the damage incurred in the accident is $0; minor claims where the damage incurred is $1000; moderate claims where the damage is $5000; and serious claims where the damage is $10,000. Suppose also that 80% of claims are trivial, 10% of claims are minor, 8% of claims are moderate, and 2% of claims are serious. If each customer has a $500 deductible, what premium should the company charge if it wants to average $100 in profit per customer?
Suppose a car insurance company divides claims from automobile accidents into four categories: trivial claims where the damage incurred in the accident is $0; minor claims where the damage incurred is $1000; moderate claims where the damage is $5000; and serious claims where the damage is $10,000. Suppose also that 80% of claims are trivial, 10% of claims are minor, 8% of claims are moderate, and 2% of claims are serious. If each customer has a $500 deductible, what premium should the company charge if it wants to average $100 in profit per customer?
Suppose a car insurance company divides claims from automobile accidents into four categories: trivial claims where the damage incurred in the accident is $0; minor claims where the damage incurred is $1000; moderate claims where the damage is $5000; and serious claims where the damage is $10,000. Suppose also that 80% of claims are trivial, 10% of claims are minor, 8% of claims are moderate, and 2% of claims are serious. If each customer has a $500 deductible, what premium should the company charge if it wants to average $100 in profit per customer?

Explanation / Answer

X : claim amount

let y denotes the average claim amount given by the company against claim

Y =X - 500

E(Y) = Expected claim amount given by the company against claim per customer.

E(Y) =E(X) - $500

E(X) = sum (X * P(X)) = $700

E(Y) = $700 -$500 = $200

Since profit = $100

Profit = Primium amount - Claim amount

100$= primium amount - $200

primium amount =$300

Comapany Should charge $300 premium if it wants to average $100 in profit per customer.

Type of Claim propertion of claim Claim amount X * P(x) Trivial Claim 80% 0 0 Minor Claim 10% $1000 100 Moderate Claim 8% $5000 400 Serious Claim 2% $10000 200 Total 100% --------- 700

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