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## Life Contingencies I

• Teacher(s):
• Course given in: English
• ECTS Credits: 6 credits
• Schedule: Spring Semester 2019-2020, 4.0h. course (weekly average)
•  sessions
•  course website
• Related programme: Master of Science (MSc) in Actuarial Science

### Objectives

This course aims at providing the students with a working knowledge of life insurance mathematics. The underlying concepts and tools are used in life insurance (including life annuities), pension funds, and social security design, valuation, and planning. At the end of the course Life Contingencies II, that is the continuation of this course, the student will be able to compute life insurance premiums, reserves, etc., build survival models (single/multiple decrements, single life or multiple lives) using stochastic and deterministic approaches.

### Contents

• Survival distributions: age at death, future lifetime, life tables, fractional ages, mortality laws, select and ultimate life tables.
• Life insurance: actuarial present value function (apv), moments of pv, basic life insurances contracts, portfolio.
• Life annuities: actuarial accumulation function, moments of pv, basic life annuities.
• Benefit premiums: actuarial equivalence principle, loss function, accumulation type benefits.
• Benefit reserves: prospective loss function, basic contracts, recursive equations, fractional durations.
• Commutation functions

### References

• Bowers, N.L. , D.A. Jones, H.U. Gerber, C.J. Nesbitt, J.C. Hickman (1997) Actuarial Mathematics, 2nd ed., Society of Actuaries, Schaumburg (IL).
• Dickson, C.M., M.R. Hardy, H.R. Waters (2013) Actuarial Mathematics for Life Contingent Risks, 2nd ed, Cambridge University Press, Cambridge.
• Cunningham, R., T.N. Herzog, R.L. London (2014) Models for Quantifying Risk, 6th ed., Actex Publications, Winsted (CT).
• Gerber, H.U. (1997) Life Insurance Mathematics, 3rd ed., Springer, Berlin.
• Jordan, C.W. (1967) Life Contingencies, 2nd ed., Society of Actuaries, Schaumburg (IL).

### Pre-requisites

Mathematics of compound interst ; Probability and Stochastic Processes

### Evaluation

#### First attempt

Exam:
Written 3h00 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Midterm exam: Optional.
Final written exam.
If the grade of the midterm exam is greater than the grade of the final exam, the final grade = 0.3 × Midterm_Exam + 0.7 × Final_Written_Exam.
If the grade at the final exam is greater than the grade of the midterm, the final grade = Final_Written_Exam.

#### Retake

Exam:
Written 3h00 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Same conditions as for the first attempt.

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