By by Bjørn Sundt.
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Extra info for An introduction to non-life insurance mathematics
One advantage of counting a multiple claim as one claim, is that it is not always obvious how to define a claim. This problem is particularly clear in comprehensive insurance forms. In a fire incidence in house-owner insurance, should damage to the building and furniture be counted as one or two claims? And should an automobile collision count one claim for third party liability, one claim for damage on own vehicle, one claim for driver's accident, etc.? The answers to such questions are not clear, and definitions vary between companies.
For given transition rules Tone should calculate the Bayes risk with different initial classes to find the optimal class. Then one should do similar calculations with other transition rules to find good rules. We see that for given bonus rules the Bayes scale is found by straightforward calculations. To find an optimal initial class one has to calculate the Bayes risk for all the K classes. This should not be too complicated in the age of computers. However, to find good transition rules one has to apply trial and error based on intuition.
How should we reinsure? In the following we shall consider N( t) as the number of claims incurred in (O,t). This means that if more than one claim occur at time s, they will be be counted as one claim. In practice we sometimes have more than one claim at the same time. Such claims are called multiple claims. One example is when several insureds are injured by the same accident. Another example is natural catastrophes like flood, hurricanes, and earthquakes that can hit a large number of policies at the same time.
An introduction to non-life insurance mathematics by by Bjørn Sundt.