Syllabus: M339U


Textbook : Actuarial Mathematics for Life Contingent Risks, 2nd Edition (2013) David C. Dickson, Mary R. Hardy, and Howard R. Waters, Cambridge University Press, ISBN 9781107044074



Completion of Probability M362K with a grade of at least C- is needed. Unless Interest Theory M329F has been completed with a grade of at least C-, concurrent enrollment is required. Likewise, unless Linear Algebra M340L or M341 has been completed with a grade of at least C-, you must take one of these concurrently with this course. 

Please note that thorough knowledge of calculus, probability, and interest theory will be assumed. 


Chapter 1 Introduction to life insurance (1 hour)

    1.1 Summary

    1.2 Background

    1.3 Life insurance and annuity contracts

    1.4 Other insurance contracts

    1.5 Pension benefits

    1.6 Mutual and proprietary insurers


Chapter 2 Survival models (4 hours)

    2.1 Summary

    2.2 The future lifetime random variable

    2.3 The force of mortality

    2.4 Actuarial notation

    2.5 Mean and standard deviation of Tx

    2.6 Curtate future lifetime


Chapter 3 Life tables and selection (5 hours)

    3.1 Summary

    3.2 Life tables 

    3.3 Fractional age assumptions

    3.4 National life tables

    3.5 Survival models for life insurance policyholders

    3.6 Life insurance underwriting

    3.7 Select and ultimate survival models

    3.8 Notation and formulae for select survival models

    3.9 Select life tables

    3.10 Some comments on heterogeneity in mortality

    3.11 Mortality trends


Chapter 4 Insurance benefits (8 hours)

    4.1 Summary

    4.2 Introduction

    4.3 Assumptions

    4.4 Variation of insurance benefits

    4.5 Relatingand 

    4.6 Variable insurance benefits

    4.7 Functions for select lives


Chapter 5 Annuities (9 hours)

    5.1 Summary

    5.2 Introduction

    5.3 Review of annuities certain

    5.4 Annual life annuities

    5.5 Annuities payable continuously

    5.6 Annuities payable 1/mthly

    5.7 Comparison of annuities by payment frequency

    5.8 Deferred annuities

    5.9 Guaranteed annuities

    5.10 Increasing annuities

    5.11 Numerical illustrations

    5.12 Functions for select lives


Chapter 6 Premium calculation (7 hours)

    6.1 Summary

    6.2 Preliminaries

    6.3 Assumptions

    6.4 The present value of future loss random variable

    6.5 The equivalence principle

    6.6 Gross premiums

    6.7 Profit

    6.8 The portfolio percentile premium principle

    6.9 Extra risks


Chapter 7 Policy values (3 hours)

    7.1 Summary 

    7.2 Assumptions

    7.3 Policies with annual cash flows


For the suggested time devoted to each chapter, 1 hour corresponds to 50 minutes of actual class time. The total number of hours listed do not constitute an entire semester. They allow for review and examinations.



Any approved calculator can be used for this class (approved list: You may use more than one calculator on this list.  


Actuarial Examinations

In conjunction with M339V, M339U covers the content of SOA Exam MLC and CAS Exam LC. Topics covered: life insurance, survival models, life tables, insurance benefits, annuities, and premium calculation. See and for further details regarding these exams.