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Life Contingencies II

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



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.


* Commutation functions

* 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.

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


* 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).


Life Contingencies I


First attempt

Written 3h00 hours
Not allowed

Grades: The final exam grade (FE) counts for 70% of the final grade (FG) if the midterm grade (30%) is greater than the final exam grade, and for 100% otherwise.

The midterm exam: Date to be announced. [Grade: MTE]

Final grade: FG := 0.7 · FE + 0.3 · max( FE , MTE ).

Documentation: No documentation allowed.


Written 3h00 hours
Not allowed

Same conditions as for the first attempt.

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