Fundamentals of Actuarial Mathematics, 3rd Edition

12 Expenses and profits

12.1 Introduction

Provision for expenses and profits are two important features that we have ignored in our models up to now. Premiums paid on insurance and annuity contracts must not only provide benefits, but must also contain an extra amount to cover the expenses of operating the business. In addition the premiums must be sufficient to generate profits as a return to the investors who provide the capital necessary to start an insurance operation.

We will begin with a discussion of expenses, and the first step is to distinguish between three basic categories of regular periodic expenses. These can depend on the premiums, on the amount of the benefits, or be constant per policy. The major expense of the first type is commissions paid to the agents selling the policies. It is traditional for their compensation to take the form of certain percentages of the premiums. There are various expenses that will depend on the amount of the benefits. For example, larger policies will require additional efforts and expenses in the selection procedure to verify that the individual is a sound risk. Finally, there are expenses, such as setting up records for a new policy, that are largely independent of the size of premiums or benefits, and are fixed for each policy.

A peculiar feature of expenses for life insurance is that a large portion of these are incurred in the first year of the policy. Commissions paid on the initial premium are traditionally much higher than ...