MA546 LongTerm Actuarial Mathematics
Course Catalog Description
Introduction
This course is designed to satisfy the Validation by ASA requirement for LongTerm Actuarial Mathematics (LTAM) Exam. The course contents comprise various aspects of long term actuarial mathematics, including, longterm insurance coverages, survival models and their estimation, present value random variables, premium calculation, reserves calculation, pension plans and retirement benefits. Discussions are also made on applying advanced probability and statistic to evaluate various longterm insurances.
Prerequisites: MA540, MA541
Crosslisting: None
Course Objective
• Understand the key features of longterm insurance coverages
• Understand key concepts concerning parametric and nonparametric (tabular) and multistate models including single life, or multiple life, and multiple decrements
• Perform calculations on the present value random variables associated with benefits and expenses for any of the models
• Use and explain premiumcalculation methodologies
• Understand reserves for insurances and annuities for models
• Understand how the previous models apply to pension plans and retirement benefits
• Catch basics of insurance and reinsurance coverages for longterm insurances
• Use basic methods to calculate premiums and reserves for longterm insurance coverages
Instructors
Teaching Associate Professor  Office  

Xiaohu Li

xli82@stevens.edu  Kidde 113A 
Campus  Fall  Spring  Summer 

On Campus  X 
More Information
Course Outcomes

• Describe the appropriate models to be used to calculate expected present values, premiums or contributions, and reserves for each longterm coverage
• Calculate nonparametric estimates of survival models using the KaplanMeier and NelsonAalen formulas for seriatim data and adaptations for grouped data
• Calculate, using both seriatim and grouped data, maximum likelihood estimates of transition probabilities assuming constant transition intensity during fixed age intervals; Calculate the variances of and construct confidence intervals for the estimators
• Apply appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler
• Calculate and interpret common profit measures such as expected profit, actual profit, gain, gain by source and period, internal rate of return, profit margin, and breakeven year
• Given particular participant data, plan provisions, and valuation assumptions, apply the concerned models to defined benefit pension plans and calculate and interpret replacement ratios, accrued benefits, gain or loss, and their expected values with adjustments such as the early retirement reduction factor
• Given particular participant data, plan provisions, and valuation assumptions, calculate and interpret the actuarial accrued liability and the normal cost for a defined benefit plan under the projected unit credit (PUC) cost method and the traditional unit credit (TUC) cost method.
• Identify and interpret the assumptions and methods for retiree health care plans. Given particular participant data, plan provisions, and valuation assumptions, calculate and interpret the expected present value of future benefits, accumulated postretirement benefit obligation (APBO), and the normal cost or service cost for retiree health care plans.
• Calculate and interpret the effect of changes in underlying valuation assumptions such as mortality, discrete salary increase changes, other decrements and interest on the quantities, and apply appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.
Course Resources
Textbook

Required textbook
Actuarial Mathematics for Life Contingent Risks, 2nd Edition, 2013 Dickson, D., Hardy, M., Waters, H Cambridge University Press, ISBN: 9781107044074.

Syllabus and study materials, SOA
Exam LTAM: LongTerm Actuarial Mathematics
Grading
Grading Policies
Weights  
1  Homework  45% 
2  Midterm  25% 
3  Final  35% 
Maximum Possible  100% 
Lecture Outline
Topic  Reading(s)  Homework  

Week 1  Longterm insurance coverages: life insurance and annuity contract, pension benefit  Chapter 1  Exercises: 1.6, 1.7 
Week 2  Survival models: force of mortality, curtate future lifetime  Chapter 2  Exercises: 2.4, 2.5, 2.7, 2.11, 2.12, 2.13, 2.15 
Week 3  Lifetime tables: fractional age, survival models for lifetime insurance policy holder, survival model selection, heterogeneity in mortality  Chapter 3  Exercises 3.1, 3.3, 3.5, 3.7, 3.9 
Week 4  Insurance benefit  Chapter 4  Exercises: 4.3, 4.6, 4.9, 4.12, 4.15, 4.18, 4.21 
Week 5  Annuities  Chapter 5  Exercises: 5.2, 5.4, 5.6, 5.8, 5.10, 5.12, 5.14, 5.16, 5. 18 
Week 6  Premium calculations  Chapter 6  Exercise: 6.3, 6.6, 6.9, 6.12, 6.15, 6.18, 6.2 
Week 7  Midterm exam  Chapters 16  
Week 8  Policy value  Chapter 7  Exercises: 7.2, 7.5, 7.8, 7.11, 7.14, 7.17, 7.20 
Week 9  Multistate models  Chapter 8  Exercises: 8.3, 8.6, 8.8, 8. 12, 8.14, 8.8 
Week 10  Joint life and last survivor benefit  Chapter 9  Exercise: 9.2, 9.4, 9. 6, 9.9, 9.11, 9.14, 9.16 
Week 11  Pension mathematics  Chapter 10  Exercises: 10.1, 10.3, 10.5, 10.7, 10.9, 10.11, 10.13 
Week 12  Emerging costs for traditional life insurance  Chapter 12  Exercises: 12.2, 12.4, 12.6, 12.8, 12.10, 12.12 
Week 13  Review  Chapters 78  
Week 14  Final exam  All chapters 