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Life Insurance Mathematics (Advanced) : Jan Dhaene

This course provides advanced study of life insurance mathematics, including theoretical concepts needed for life insurance actuaries. It extends basic survival distributions, life tables, and insurance/annuity models to include general statuses dependent on multiple lives. Multiple decrement models are developed to account for withdrawals, death, disablement, and retirement. Markov models generalize to allow transitions between states. Models incorporating expenses are developed using equivalence principles between gross premiums and benefits/costs. Contract alterations like universal and unit-linked insurance transferring investment risk are examined. Profit testing and embedded value calculations are also discussed. Exams are written and materials include several technical actuarial texts.

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75 views2 pages

Life Insurance Mathematics (Advanced) : Jan Dhaene

This course provides advanced study of life insurance mathematics, including theoretical concepts needed for life insurance actuaries. It extends basic survival distributions, life tables, and insurance/annuity models to include general statuses dependent on multiple lives. Multiple decrement models are developed to account for withdrawals, death, disablement, and retirement. Markov models generalize to allow transitions between states. Models incorporating expenses are developed using equivalence principles between gross premiums and benefits/costs. Contract alterations like universal and unit-linked insurance transferring investment risk are examined. Profit testing and embedded value calculations are also discussed. Exams are written and materials include several technical actuarial texts.

Uploaded by

EL Hafa Abdellah
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Life Insurance Mathematics (Advanced)

Jan Dhaene

Aims
This course provides a rigorous study of advanced topics in life insurance mathematics. It offers
the student the theoretical concepts needed by a life insurance actuary.

Prerequisites
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Operational knowledge of probability theory and statistics.


Knowledge of basic life insurance theory.

Contents
The course starts with a brief overview of basic life insurance theory: survival distributions and
life tables, life insurance, life annuities, net premiums and net premium reserves.
The basic theory is first extended to insurance and annuities on a general status, with benefits
and premium payment plans dependent on several lives. Multiple life functions depending on
joint-life and last survivor statuses are studied, as well as insurance products where the order of
death determines the benefits and premium payments.
In basic life insurance theory, individual lives (or statuses) are subject to a single decrement of
death. Multiple decrement models are developed for situations where a single life is subject to
multiple decrements (withdrawal, death, disablement, retirement). A major application of
multiple decrement models in actuarial science can be found in the theory of pension plans. We
consider basic methods used in calculating the actuarial present value of benefits and
contributions for a participant in a pension plan. The multiple decrement model is generalized to
the Markov model for life contingencies where transitions between different states are possible in
both directions.
The main cash outflows for an insurer are the benefits to be paid out upon survival or death of
the insured. But an insurer has also cash outflows related to expenditures. Insurance models
including expenses start from the equivalence principle to establish an actuarial equivalence
between gross premiums at the one hand, and benefits and costs at the other hand. Gross
reserves, surrender values and zillmerised reserves are considered in detail.
Conventional insurance contracts are contracts where the benefits (upon survival or death) as
well as the premiums are known (deterministic) at policy issue. For such contracts, the
investment risk is taken by the insurer. We investigate several alterations of the classical life
insurance. Universal life insurance contracts offer more flexibility compared to conventional
contracts in the sense that premium payments are not fixed at policy issue. In Unit-linked life
insurance contracts the investment risk is (partially) taken by the policyholder.
The concept of Fair Valuation of life insurance liabilities is discussed.
Profit testing is a technique used for determining expected profits of a given contract
(conventional or unit linked). It is used to determine premiums and/or cost structure of a contract
(conventional or unit-linked) such that a predetermined profit target is reached.
Attention is also given to Embedded Value calculations (calculation of the Present Value of
Future Profits and of the Net Asset Value).
.

Exam
Written exam.

Reading Material
-

Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., (1997). Actuarial
Mathematics. The Society of Actuaries, Itacsa, Illinois. Second edition.
De Vijlder, F.E. (1997). Life Insurance Theory: Actuarial Perspectives. Kluwer Academic
Publishers, Boston, Dordrecht, London, pp. 184.
Gerber, H.U. (1995). Life Insurance Mathematics. Second edition, Springer, Swiss
Association of Actuaries, pp. 217
Hardy, M. (2003). Investment Guarantees: Modeling and Risk Management for EquityLinked Life Insurance. Wiley, pp. 286.
Mller, T.; Mogens, S. (2007). Market-Valuation Methods in Life and Pension Insurance.
CambridgeUniversity Press, pp. 279.
Wolthuis, H. (1994). Life Insurance Mathematics, the Markovian Model. Caire Education
Series 2, Brussels, pp. 255.

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