Significant models of claim amount Introduction Very important

Significant models of claim amount Introduction Very important for insurance companies to know the distribution of claim amount. Theoretically it will be enough to consider non-negative variate with integer value, but in the practice if the claim amount would be huge then it is usual to use absolute continuous distributions. When we are trying to fit distributions of claim amount we have to consider that the claims handling process is usually a long-term process and in advance we do not know the ultimate claim payment. Between the occurring date, reporting date and paying date would be long especially in complex claim event. It means that usually the claims with longer process are more than the claims with short-periods process. Insurance mathematics X. lecture

Significant models of claim amount Classical models I. Usually there is not fitting so well to claim data, but the using of exponential distribution is comfortable. We can estimate the parameter just from first empiric moment and the calculation is not so complicated. Insurance mathematics X. lecture

Significant models of claim amount Classical models II. Insurance mathematics X. lecture

Significant models of claim amount Classical models III. Insurance mathematics X. lecture

Significant models of claim amount Classical models IV. Insurance mathematics X. lecture

Significant models of claim amount Classical models V. Insurance mathematics X. lecture

Significant models of claim amount Classical models VI. Insurance mathematics X. lecture

Significant models of claim amount Retention I. According to a lot of nonlife product it usually is used retention. The insured are more concerned to save his/her assets if they have to pay a part of claim – this is the first reason why the using of retention is so popular. The second reason is that there are less claim event (mainly if there a bonus system also) and the claim handling department can focus deeper the major claims. There are two version of retention: insured will pay p% of the total claim or c fixed amount per claim (sometimes mixed version occurs). Insurance mathematics X. lecture

Significant models of claim amount Retention II. Insurance mathematics X. lecture

Significant models of claim amount Retention III. Insurance mathematics X. lecture

Significant models of claim amount Retention IV. From this equation we will get the probability density function as next: It means that the type of distribution was changed. Insurance mathematics X. lecture

Significant models of claim amount Retention V. Insurance mathematics X. lecture

Significant models of claim amount Retention VI. Pareto distribution Insurance mathematics X. lecture

Significant models of claim amount Retention VII. It means that the type of distribution of claim amount will not change. The new expected value and variance will be as follows: Insurance mathematics X. lecture

Significant models of claim amount Inflation I. The claim experience comes from the past, but the projection goes to the future. It means if we would like to calculate an adequate estimation then we have to take into consideration the time-value of money. The most plausible process to use inflation index. But finding adequate inflation indices is a difficult task, because we have to find a figure which is corresponding the claims related to given product or business lines. If we are finding an adequate figure then the above used distribution will be changed as follows (but the type of distribution is not changing). Insurance mathematics X. lecture

Significant models of claim amount Inflation II. Insurance mathematics X. lecture