An auto insurer has analyzed claim experience and has chosen as a model for aggregate daily...

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An auto insurer has analyzed claim experience and has chosen as a model for aggregate daily claims a compound Poisson random variable with an average of 20 claims per day. The insurer will pay the full amount of damage when a claim is made. and the claim is modeled to be exponentially distributed with a mean claim amount of $1000. The company considers offering a policy with a deductible amount of $250 (i.e., if damage occurs, the company will pay the amount of damage that is in excess of $250). The company charges an aggregate premium (divided equally among all policy holders) that is one standard deviation larger than the expected aggregate claim. What percentage reduction in premium results if all policyholders switch from full coverage to the coverage with $250 deductible. A) 10% B) 15% C) 20% D) 25% E) 30% An auto insurer has analyzed claim experience and has chosen as a model for aggregate daily claims a compound Poisson random variable with an average of 20 claims per day. The insurer will pay the full amount of damage when a claim is made. and the claim is modeled to be exponentially distributed with a mean claim amount of $1000. The company considers offering a policy with a deductible amount of $250 (i.e., if damage occurs, the company will pay the amount of damage that is in excess of $250). The company charges an aggregate premium (divided equally among all policy holders) that is one standard deviation larger than the expected aggregate claim. What percentage reduction in premium results if all policyholders switch from full coverage to the coverage with $250 deductible. A) 10% B) 15% C) 20% D) 25% E) 30%

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