Syllabus: M339V


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


Responsible party: Mark Maxwell August 2014


Description of the Course: M 339V = M 389V Actuarial Contingent Payments II. ?Topics covered: Policy Values, Multiple State Models, Pensions, Interest Rate Risk, and Emerging Costs for Traditional Life Insurance.  

This is an actuarial capstone course and students are expected to do some independent learning and improve verbal and written acumen.  Three graded components of the course are 1) communication, 2) content, and 3) contribution to class.  This class carries the Independent Inquiry Flag.  This class carries the Quantitative Reasoning flag.  

Meets with M389V, the corresponding graduate-course number.  Offered every spring semester only. This is a 3-credit course.



Completion M 329F and M 339U with a grade of at least C-. 

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


Topics Covered

Chapter 7 Policy values 

       7.4 Policy values for policies with cash flows at 1/mthly intervals 

       7.4.1 Recursions 

       7.4.2 Valuation between premium dates 

       7.5 Policy values with continuous cash flows

       7.5.1 Thiele’s differential equation 

       7.5.2 Numerical solution of Thiele’s differential equation 

       7.6 Policy alterations 

       7.7 Retrospective policy values 

       7.7.1 Prospective and retrospective valuation 

       7.7.2 Defining the retrospective net premium policy value 

       7.8 Negative policy values 

       7.9 Deferred acquisition expenses and modified premium reserves 

       7.10 Notes and further reading 

       7.11 Exercises 


Chapter 8 Multiple state models 

       8.1 Summary 

       8.2 Examples of multiple state models 

       8.2.1 The alive–dead model 

       8.2.2 Term insurance with increased benefit on accidental death 

       8.2.3 The permanent disability model 

       8.2.4 The disability income insurance model 

       8.3 Assumptions and notation 

       8.4 Formulae for probabilities 

       8.4.1 Kolmogorov’s forward equations 

       8.5 Numerical evaluation of probabilities 

       8.6 Premiums 

       8.7 Policy values and Thiele’s differential equation 

       8.7.1 The disability income insurance model 

       8.7.2 Thiele’s differential equation – the general case 

       8.8 Multiple decrement models 

       8.9 Multiple decrement tables 

       8.9.1 Fractional age assumptions for decrements 

       8.10 Constructing a multiple decrement table 

       8.10.1 Deriving independent rates from dependent rates 

       8.10.2 Deriving dependent rates from independent rates 

       8.11 Comments on multiple decrement notation 

       8.12 Transitions at exact ages 

       8.13 Markov multiple state models in discrete time 

       8.13.1 The Chapman–Kolmogorov equations 

       8.13.2 Transition matrices 

       8.14 Notes and further reading 

       8.15 Exercises 


Chapter 9 Joint life and last survivor benefits 

       9.1 Summary 

       9.2 Joint life and last survivor benefits 

       9.3 Joint life notation 

       9.4 Independent future lifetimes 

       9.5 A multiple state model for independent future lifetimes 

       9.6 A model with dependent future lifetimes 

       9.7 The common shock model 

       9.8 Notes and further reading 

       9.9 Exercises 


Chapter 10 Pension mathematics  

       10.1 Summary 

       10.2 Introduction 

       10.3 The salary scale function 

       10.4 Setting the DC contribution 

       10.5 The service table 

       10.6 Valuation of benefits 

       10.6.1 Final salary plans 

       10.6.2 Career average earnings plans 

       10.7 Funding the benefits [Not covered on SOA exam MLC]

       10.8 Notes and further reading 

       10.9 Exercises 


Chapter 11 Yield curves and non-diversifiable risk  

       11.1 Summary 

       11.2 The yield curve 

       11.3 Valuation of insurances and life annuities 

       11.3.1 Replicating the cash flows of a traditional non-participating product 

       11.4 Diversifiable and non-diversifiable risk 

       11.4.1 Diversifiable mortality risk 

       11.4.2 Non-diversifiable risk 

       11.5 Monte Carlo simulation [Not covered on SOA exam MLC]

       11.6 Notes and further reading 

       11.7 Exercises 


Chapter 12 Emerging costs for traditional life insurance  

       12.1 Summary 

       12.2 Introduction 

       12.3 Profit testing a term insurance policy 

       12.3.1 Time step 

       12.3.2 Profit test basis 

       12.3.3 Incorporating reserves 

       12.3.4 Profit signature 

       12.4 Profit testing principles 

       12.4.1 Assumptions 

       12.4.2 The profit vector

       12.4.3 The profit signature 

       12.4.4 The net present value 

       12.4.5 Notes on the profit testing method 

       12.5 Profit measures 

       12.6 Using the profit test to calculate the premium 

       12.7 Using the profit test to calculate reserves 

       12.8 Profit testing for multiple state models 

       12.9 Notes 

       12.10 Exercises 


Chapter 13 Participating and Universal Life insurance 

       13.1 Summary 

       13.2 Introduction 

       13.3 Participating insurance 

       13.3.1 Introduction 

       13.3.2 Examples 

       13.3.3 Notes on profit distribution methods 

       13.4 Universal Life insurance 

       13.4.1 Introduction 

       13.4.2 Key design features 

       13.4.3 Projecting account values 

       13.4.4 Profit testing Universal Life policies 

       13.4.5 Universal Life Type B 

       13.4.6 Universal Life Type A 

       13.4.7 No-lapse guarantees 

       13.4.8 Comments on UL profit testing 

       13.5 Comparison of UL and whole life insurance policies 

       13.6 Notes and further reading 

       13.7 Exercises 



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.