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Life Contingencies I

  • Teacher(s): F.Dufresne
  • Course given in: English
  • ECTS Credits: 6 credits
  • Schedule: Spring Semester 2018-2019, 4.0h. course (weekly average)
  •  séances
  • site web du cours course website
  • Related programme: Master of Science (MSc) in Actuarial Science



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.


  • 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


  • 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).


Mathematics of compound interst ; Probability and Stochastic Processes


First attempt

Written 3h00 hours
Not allowed
Allowed with restrictions

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

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

Mid-term assignment: 3 or 4 small “projects” to be done with VBA, R, Python, Maple, or any other programming language or mathematical software. Note: An assignment might not require the use of programming. [Grade MTA]


The student has to do at least three (3) of the assignments to be admitted to the exam. The student’s solutions of the (attempted) assignments do not have to be perfect but must demonstrate a sufficient knowledge of the topic (i.e., the student must obtain a “pass” mark, if not she/he has to do some additional work on the assignment).

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


Written 3h00 hours
Not allowed
Allowed with restrictions

Same conditions as for the first attempt.

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