What is life math

Life actuarial



Chapter 1. Introduction

Before we dive into the subject of German life insurance technology, let us first set up this work. This is followed by a short list of books that the author considers worth mentioning due to his own training and professional activity.

Chapter 2. Classification

Most European life insurance companies implement their products and the associated insurance policies in a cash flow projection model (CFPM for short). At this point, an introductory explanation should be given of why insurance companies go to great lengths to implement this.

Chapter 3. Basics of Life Insurance

What is insurance or insurance? There are numerous definitional answers to this question, and these inevitably lead to the field of insurance science or insurance management. However, we don't want to go too far here.

Classic life actuarial math


Chapter 4. Elementary Financial Mathematics

Since life insurance mathematics is based on financial mathematics, the basis for the following chapters is laid here on the one hand and the "interest" calculation basis is considered on the other. In the appendix (see Appendix B) there is an overview of helpful formulas that are regularly used in the context of financial mathematical calculations.

Chapter 5. Biometric Basics

In the previous chapter, the interest calculation basis was considered. We will now look at the second component of the calculation bases, biometrics. The biometric component encompasses all types of risks to which an individual is exposed, e.g. death, occupational disability, marriage or retirement.

Chapter 6. Expected Present Values

Based on the two calculation bases of interest and biometrics, we are now able to derive present values ​​for various insurance products. More precisely, these are expected cash values, since it is not certain whether and when the insurance benefit is to be paid. Present values ​​of pension benefits will later also be used as premium present values.

Chapter 7. Costs, Surcharges, and Commissions

In this chapter we consider the costs associated with an insurance contract and thus - after interest and biometrics - the last of the three calculation bases.

Chapter 8. Rewards

Now that we have got to know all the calculation bases in the previous chapters, we can now determine the premiums for the various insurance products. Brief repetition: the premium, synonymous with the contribution, is the price that the policyholder has to pay for transferring the risk of death and / or survival or longevity to the insurer. If the insured event occurs, CC pays the guaranteed benefit to the beneficiary.

Chapter 9. Cover capital and other reserves

By selling a life insurance policy, the insurance company makes a guarantee promise. In the case of capital life or risk insurance, the insurer promises a benefit in the event of death or experience. In the case of a pension insurance, the guarantee consists of the regular, usually lifelong, payment of a predetermined amount. The guarantee often extends over a long period of 40, 60 or even more years.

Chapter 10. Profit sharing

Since the expected cash value of the incoming bonuses corresponds to the expected cash value of the payments (for services and costs), an expected profit of zero follows from the validity of the principle of equivalence.

Advanced insurance technology


Chapter 11. Changes to the Contract and Warranty Values

During the long term of a life insurance contract, there are often changes in personal circumstances at the policyholder or changes in the financial markets, which can also have an impact on the existing contractual relationship. For example, trust in the account manager or even the insurance company itself can dwindle. Or the customer prefers a form of investment with a higher return.

Chapter 12. Connected Lives

So far, we have only considered the case that a single person is exposed to the risk of mortality. That is why one also says: “a life that is at risk”. As described in Sect. 3.2, however, it often happens - especially in the area of ​​company retirement provision or pension insurance - that “several lives at risk” are considered, which is referred to as connected lives.

Chapter 13. Unit-Linked Insurance

Well-known insurances such as the endowment life insurance or the (deferred) annuity insurance are called classic or conventional insurance because their actuarial reserves are calculated and managed according to the classic or conventional approach. In this chapter we want to look at a type of product that has made its way into the product landscape of German life insurance since deregulation in 1994, namely unit-linked insurance. They have become an indispensable part of VU's product portfolio and some of them have reached a considerable volume.

Chapter 14. Disability Insurance

The occupational disability insurance (short: BU insurance or BUV) is also an integral part of the product range offered by most life insurers. In the following, the term always includes disability insurance (short: EU insurance or EUV), which is based on a different degree of inability to earn an income, but otherwise has identical characteristics as the BU insurance.

Chapter 15. Long term care insurance

In the area of ​​life insurance, long-term care insurance has been experiencing a renaissance for a number of years or is gaining new momentum within the VU product range.

Chapter 16. Life reinsurance

Reinsurance (short: RV) or assignment describes the process in which a primary insurer passes on or assigns part of the risks it has assumed to another insurance company. The primary insurance company is referred to as the assignor, the receiving reverse insurance company as the assignee (seldom also assignee). If a reinsurer in turn cedes risks to another reinsurer, this transfer is called further reinsurance or retrocession, the transferring reinsurer is called retrocedent and the receiving reinsurer is called retrocessionaire.

Chapter 17. Accounting

At the end of the book, various aspects are considered, which are summarized under the more general term of accounting. For example, we will deal with the preparation of the annual financial statements of an insurance company, the notification and reporting obligations that exist towards the supervisory authority and explain the solvency requirements to which an insurance company is subject.

Chapter 18. Projection Models

Cash flow projection models or projection models have numerous areas of application and are used, for example, in the following actuarial questions and activities.



Chapter 19. Biometric calculation bases

The first order biometric calculation bases used in the context of the book are tabulated in this appendix. If commutation numbers are given, these were calculated on the basis of a fictitious discount rate of i = 2%.

Chapter 20. Basic mathematical formulas

This section lists well-known formulas that are regularly used in the context of financial and actuarial calculations.

Chapter 21. Dictionary German - English

Dictionary German - English