TABLE OF CONTENTS The activities of an insurer can be described as an input-output system, in which the surplus increases because of (earned) premiums and interest, and decreases because of claims and costs, see also the previous chapter. In this chapter we discuss some mathematical methods to determine the premium from the distribution of the claims. The actuarial aspect of a premium calculation is to calculate a minimum premium, sufficient to cover the claims and, moreover, to increase the expected surplus sufficiently for the portfolio to be considered stable.
B hlmann (1985) described a top-down approach for the premium calculation. One primarily looks at the premium required by the total portfolio. Secondly, one considers the problem of spreading the total premium over the policies in a 'fair' way. To determine the minimum annual premium, we use the discrete ruin probability as introduced in the previous chapter (with some simplifying assumptions). The result is an exponential premium (see Chapter 1), where the parameter follows from the maximal ruin probability allowed and the initial capital. Assuming that the suppliers of the initial capital are to be rewarded with a certain annual dividend, and that the resulting premium should be as low as possible, therefore as competitive as possible, we can derive the optimal initial capital. Furthermore we show how the total premium can be spread over the policies in a fair way, while the total premium keeps meeting our objectives.
For the policy premium, a lot of premium principles can be justified. Some of...
