Introduction

We consider in this chapter the general type of life insurance where premiums and benefits are calculated provisionally at issuance of the policy and later determined according to the performance of the insurance contract or company. The determination of premiums and benefits can take various forms depending on the type of contract. Examples are various types of participating life insurance (in some countries called with-profit life insurance) and various types of pension funding.

The determination of premiums and benefits is based on payment of dividends, which in general may be positive or negative, from the insurance company to the policy holder. It is important to distinguish between two aspects of the determination: the dividend plan and the bonus plan. The dividends plan is the plan for allocation of dividends. However, often the dividends are not paid out immediately in cash but are converted into a stream of future payments. The bonus plan is the plan for how the dividends are eventually turned into payments.

In Steffensen (2000), a framework of securitization is developed where reserves are no longer defined as expected present values but as market prices of streams of payments (which, however, happen to be expressible as expected present values under adjusted measures). An insurance contract is defined as a stream of payments linked to dynamic indices, covering a wide range of insurance contracts including various forms of unit-linked contracts.