Coinsurance is the fraction of losses covered by the policy. For example, means if a loss is incurred, 80% will be paid by the insurance company. A claims limit is the maximum amount that will be paid. The order in which coinsurance, claims limits, and deductibles is applied to a loss is important and will be specified by the problem. The expected payment per loss when all three are present in a policy is given by
where is the payment variable and is the original loss variable. The second moment is given by
The second moment can be used to find the variance of payment per loss. If inflation is present, multiply the second moment by and divide and by . For payment per payments, divide the expected values by or .