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## Life Contingencies II

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

[warning] This course syllabus is currently edited by the professor in charge. Please come back in a few days. --- For your information only, here is the old syllabus :

### Objectives

This series of two courses 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 last part of this course (Life Contingencies II), the student will be able to compute life insurance premiums, reserves, etc., build survival models (single/multiple decrements) using stochastic and deterministic approaches.

### Contents

* Benefit reserves and their analysis. Recursions. Risk decomposition. Interim reserves.

* Multiple life functions: joint-life, last-survivor; insurance and annuity benefits; special mortality assumptions; models for dependence of future lifetimes.

* Multiple decrement models: stochastic and deterministic approaches, associated single decrement, fractional durations.

* Multiple-state models.

* Applications of multiple decrements models: Valuation theory for pension plans.

* Insurance models including expenses.

* Commutation functions

* Introduction to Life Insurance Risk Management [if time permits]

### 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).

* Cunningham, R., T.N. Herzog, R.L. London (2005) Models for Quantifying Risk, ACTEX Publications, Winsted (CT).

* Dickson, C.M., M.R. Hardy, H.R. Waters (2013) Actuarial Mathematics for Life Contingent Risks, 2nd ed., Cambridge University Press, Cambridge.

* 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

Life Contingencies I

### Evaluation

#### First attempt

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

Grades: The final exam (FE) counts for 65% of the points if the mid-term test result (25%) and the mid-term assignments (10%) are globally better, and for 100% otherwise.

The mid-term exam: Date to be announced. [Grade: MTE]

Mid-term assignments: 3 small projects to be done with any mathematical software (Maple, Mathematica, MathLab) or programming language, e.g. VBA under Excel, R or Java. [Grade MTA]

Final grade: FG := (65/100) · FE + (35/100) · max( FE , ( 25 · MTE + 10 · MTA)/35 );

Condition to be admitted to the Final Exam: To be admitted to the final exam, the student must have done the three assignments and obtained a passing mark on each of these assignments. The student is allowed to redo the assignment in order to achieve the requested grade.

Documentation: No documentation allowed.

#### Retake

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

Same conditions as for the first attempt.

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