1.1 INTRODUCTION

The insurance industry exists because people are willing to pay a price for being insured which is higher than their expected claims. As a result, an insurer collects a premium that is larger than the expected claim size. In this chapter, we sketch an economic theory that explains why insureds are willing to pay a premium that is larger than the net premium, i.e., the mathematical expectation of the insured loss. The theory that explains this phenomenon postulates that a decision maker, generally without being aware of it, attaches a value u( w) to his wealth w instead of just w, where u( ) is called his utility function. If the decision maker has to choose between random losses X and Y, then he compares E[ u( w - X)] with E[ u( w - Y)] and chooses the loss with the highest expected utility. With this model, the insured with wealth w is able to determine the maximum premium P ⁺ he is prepared to pay for a random loss X. This is done by solving the equilibrium equation E[ u( w - X)] = u( w - P). At the equilibrium, he doesn't care, in terms of utility, whether he is insured or not. The model applies to the other party involved as well. The insurer, with his own utility function and perhaps...