## Syllabus: M339V

ACTUARIAL CONTINGENT PAYMENTS II

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.

Prerequisites:

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

7.5 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

7.11 Exercises

Chapter 8 Multiple state models

8.1 Summary

8.2 Examples of multiple state models

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

8.7 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

8.15 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

9.5 A multiple state model for independent future lifetimes

9.6 A model with dependent future lifetimes

9.7 The common shock model

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]

10.9 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]

11.7 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

13.7 Exercises

Calculators

Any approved calculator can be used for this class (approved list: http://www.soa.org/Education/Exam-Req/exam-day-info/edu-calculators.aspx). 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 https://www.soa.org/education/exam-req/edu-asa-req.aspx and http://www.casact.org/admissions/exams/ for further details regarding these exams.