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Fundamentals of Actuarial Mathematics, 3rd Edition by S. David Promislow

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22 Risk assessment

22.1 Introduction

The previous chapter was largely devoted to computing or approximating the distribution of aggregate claims for the losses on an insurance portfolio. The next problem that arises is to effectively use this information to assess and manage the risk associated with the insurer’s commitment to pay these losses. Similarly, a consumer is interested in assessing the extent to which their risk is transferred by the purchase of insurance. We alluded to this theme somewhat in Part II of the book but we now wish to investigate some of the issues in more detail. Our concentration will be on a more general basic question that has application in many areas. Given two or more uncertain alternatives, how do we compare or measure the amount of risk associated with each? This is a large topic and we confine ourselves here to a survey of some of the main ideas. It is important in what follows to distinguish between two cases. The quantities in question may involve losses in which case less is better, or gains, in which case more is better. We could conventionally fix one or the other, by introducing minus signs, but that complicates the notation, so we rely on the context to clarify what is intended. We start in the next section by talking about gains.

22.2 Utility theory

One method which may seem natural for deciding between two random payouts is to compare the expected amounts that you will receive. However, this does not always give reasonable answers ...

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