1 Introduction and motivation

1.1 Risk and insurance

In this book we deal with certain mathematical models. This opening chapter, however, is a nontechnical introduction, designed to provide background and motivation. In particular, we are concerned with models used by actuaries, so we might first try to describe exactly what it is that actuaries do. This can be difficult, because a typical actuary is concerned with many issues, but we can identify two major themes dealt with by this profession.

The first is risk, a word that itself can be defined in different ways. A commonly accepted definition in our context is that risk is the possibility that something bad happens. Of course, many bad things can happen, but in particular we are interested in occurrences that result in financial loss. A person dies, depriving family of earned income or business partners of expertise. Someone becomes ill, necessitating large medical expenses. A home is destroyed by fire or an automobile is damaged in an accident. No matter what precautions you take, you cannot rid yourself completely of the possibility of such unfortunate events, but what you can do is take steps to mitigate the financial loss involved. One of the most commonly used measures is to purchase insurance.

Insurance involves a sharing or pooling of risks among a large group of people. The origins go back many years and can be traced to members of a community helping out others who suffered loss in some form or other. For example, ...

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