The process of pricing insurance commences by the actuary trying to estimate the severity distribution and frequency for a particular insurance group. This process starts with analysing past experience. This past experience data is collected either from the insurance group, or another group as close to the concerned insurance group as possible. The reliability of this past experience as a predictor of future trends should also be considered, since the more reliable it is, the better it will predict underlying probability distributions.
The following example illustrates this: An actuary is attempting to predict the probability that a 65-year old man will die in two years. The actuary would then gather data using a large sample of 65-year old men from previous years and see how many died within a year. The probability would be given by the ratio of the number of deaths in the sample to the sum total of 65-year old men in the same sample. According to the Central Limit Theorem, if the underlying distribution has a mean p, standard deviation σ and sample size n, then the mean of the sample is approximately distributed with mean p and standard deviation σ/√n. Clearly, the larger the sample size, the smaller the variation between sample mean and the underlying value of p.
The frequency and severity distribution thus developed are combined to determine loss distribution. After reflecting provisions in the policies, such as benefit limits, the loss distribution can then be adjusted to derive the claim payment distribution. Future inflation needs to be estimated and so does expected investment returns in case premiums are invested to cover claim payments.
Now the actuary can calculate net premiums. A sufficient margin is then built in, to cover insurer’s expenses and an acceptable level of unanticipated claim payments to arrive at gross premiums.
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