Estimation of Stop Loss Premium in Fire Insurance

The estimation of stop loss premiums can be based on some knowledge about the distribution function of the sum of all claims in a year (assuming that the stop loss insurance relates to a period of one calender year). Generally speaking there are two methods to obtain this knowledge about the distribution function.1. The first method is to construct a distribution function from data concerning:a. the distribution function of the number of claims per year, taking into account the variability of the parameter(s) of this distribution function.b. the distribution function of the insured sums.c. the distribution function of partial claims.d. the correlation between the insured sum and the probability of occurring of a claim.e. the probability of contagion.2. The second method is to derive a distribution function from the year's totals of claims over a long series of years, expressed in e.g: units of the totals of insured sums in that years.In practice it is often difficult to find a useful basis to apply one of these methods. Data concerning the distribution function of the number of claims per year, of the insured sums, and of partial claims are mostly available, but often nothing is known about the correlation between the insured sum and the probability of occurring of a claim.The second method is mostly not applicable because, if the year's totals of claims over a long series of, by preference recent, years are available, these data often turn out to be heterogeneous or to be correlated with time. If, in that case, only the data of the most recent years are used, the number of these data is often a too small basis for the construction of a distribution function.