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

* Commutation functions

* Benefit reserves and their analysis.

* 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; including modified reserves systems.

* Mortality modeling, Lee-Carter model

References

* Bowers, N.L. , D.A. Jones, H.U. Gerber, C.J. Nesbitt, J.C. Hickman (1997) Actuarial Mathematics, 2nd edition, Society of Actuaries, Schaumburg (IL).

* Dickson, C.M., M.R. Hardy, H.R. Waters (2021) Actuarial Mathematics for Life Contingent Risks, 3rd edition, 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 1h45 hours

Documentation:

Not allowed

Calculator:

Allowed

Evaluation:

Midterm + final written exams

No documentation allowed

Calculators allowed

Final grade = 0.3 * max (Exam_midterm, Exam_final) + 0.7 * Exam_final.

Retake

Exam:

Written 3h00 hours

Documentation:

Not allowed

Calculator:

Allowed

Evaluation:

Written exam

No documentation allowed

Calculators allowed

Final grade = Final exam grade