2Introduction

2Introduction - 1 Introduction 1.1 Rating of Risks and...

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1 Introduction 1.1 Rating of Risks and Claims Experience in Insurance The basic idea underlying insurance is that individuals, who have the “same” exposure to a particular risk, join together to form together a “community- at-risk” in order to bear this perceived risk. In modern society, this idea is most often realized in the form of insurance. On payment of a premium, the individuals in the “community-at-risk” transfer their risk to an insurance company. We consider an insurance company with a portfolio consisting of I insured risks numbered i =1 , 2 ,...,I .Inawe l l -de f ned insurance period, the risk i produces a number of claims N i , with claim sizes Y ( : ) i ( : , 2 ,...,N i ) , which together give the aggregate claim amount X i = P N i : =1 Y ( : ) i . We will refer to the premium payable by the insured to the insurer, for the bearing of the risk, as the gross premium. The premium volume is the sum, over the whole portfolio, of all gross premiums in the insurance pe- riod. The basic task underlying the rating of a risk is the determination of the so-called pure risk premium P i = E [ X i ] .O f t en ,w eu s eju s tth et e rm “risk premium”. The classical point of view assumes that, on the basis of some objectively quanti f able characteristics, the risks can be classi f ed into homogeneous groups (risk classes), and that statistical data and theory (in particular, the Law of Large Numbers) then allow one to determine the risk premium to a high degree of accuracy. In reality, of course, it is clear that a huge number of factors contribute to the size of the risk premium. In order to have reasonably homogeneous risk classes, one would have to subdivide the portfolio into a very large number of classes. For example, if we were to use four characteristics to rate the risk, then assuming that each characteristic had 10 possible values, this would lead
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2 1 Introduction to 10 000 risk classes. Many of these classes, by their very de f nition, will contain very few risks and will therefore provide little statistical information for rating future risks. On the other hand, if we subdivide the portfolio into larger classes, the assumption of homogeneous risk pro f les within the classes becomes a f ction. In fact, it is clear that no risk is exactly the same as an- other. For example, every car driver is an individual with his own personal associated risk which is in F uenced by many factors, not least his particular character and constitution. This observation leads to the following thesis. Thesis: There are no homogeneous risk classes in insurance. Indeed in practice, relatively few so-called risk characteristics are explicitly used in the rating of risks. The segmentation of risk classes is relatively coarse. There are a number of reasons why some characteristics, which would perhaps be useful in determining the quality of a risk, are not considered.
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2Introduction - 1 Introduction 1.1 Rating of Risks and...

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