Life Contingencies


To be able to calculate the probability of death or survival of one or more persons.
To know the several types of annuities.
To deduct the formula for any type of annuities.
To know the main types of life insurance products.
To calculate the actuarial value for a life insurance product.
To know the different types of premiums and know how to calculate them.

General characterization





Responsible teacher

Pedro Alexandre da Rosa Corte Real


Weekly - 4

Total - 70

Teaching language



Mathematical Analysis I and II. Probability and Statistics at universitary medium level.


• Bowers, Newton, Gerber, Hickman, Jones and Nesbitt. Actuarial mathematics (second edition). Itasca, Illinois: The Society of Actuaries, 1997.

• Dickson, D.C.M., Hardy, M.R. and Waters, H.R.. Actuarial Mathematics for Life Contingent Risks. Cambridge University Press, 2009

• Garcia, J.A. e Simões, O.A.. Matemática Actuarial: Vida e Pensões. Almedina. 2010

• Gerber, Hans U. Life insurance mathematics (third edition). Springer-Verlag, Berlin, 1997.

• Neill, A. Life contingencies. Butterworth-Heinemann, Oxford, 1992.

Teaching method

In the theoretical and practical lectures, it will be explained and discussed the successive topics of the course program. The topics are introduced by the teacher, consolidated using as much as possible with real examples drawn from the insurance industry, followed by a brief discussion and use of computational means to support problem solving.

Evaluation method

Two tests, to be carried out during the academic period and exam (s) according to the academic calendar.

Each of the tests has a weight of 40% for the calculation of the final grade, being exempt from examination the student who has a weighted average greater than or equal to 9.5, with both tests graded at least 7.5 values.

A workgroup with report delivery and discussion with a weight of 20% of the grade.

All elements (2 tests and group assignment) are mandatory for exam waiver.

Presential tests and exams, with consultation of all paper-based material (open-book) that students want to use. If there is a component that requires computer support, students will be able to use their pc or pc in the laboratory, without access to the internet.

Subject matter

1. Survival Models
1.1. The future lifetime random variable
1.2. The force of mortality
1.3. Mortality Tables
1.4. Extra Risks/Reduction of Risks
1.5. Probabilities of death and survival for fractional ages
1.6. Probabilities of death and survival for groups of individuals
2. Life Annuities
2.1. Actuarial Present Value
2.2. Annual Life Annuities with Constant Terms
2.3. Increasing/Decreasing Life Annuities
2.4. Annuities payable m times per year
2.5. Annuities for groups of individuals
2.6. Reversible Life Annuities
2.7. Amortization scheme Annuity Certain
3. Life Insurance
3.1. Introduction
3.2. Life Insurance in case of life
3.3. Life Insurance in case of death
3.4. Mixed Life Insurance
4. Premium Calculation
4.1. Types of Premiums
4.2. The actuarial equivalence principle
4.3. Leveled Premiums
4.4. Reimbursement of Premiums paid
4.5. Expenses


Programs where the course is taught: