Math 419B Actuarial Mathematics II Winter 2013 Bouillon 101 M. W. F. 11:00 11:50

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1 Math 419B Actuarial Mathematics II Winter 2013 Bouillon 101 M. W. F. 11:00 11:50 1 Instructor: Professor Yvonne Chueh Office: Bouillon 107G (Tel: ) chueh@cwu.edu Office hours: M-Th 1-1:50 and by appointments. Schedule on Prerequisite: Math 419A and permission. Two texts required: 1. Cunningham, R.J., Herzog, T.N., and London, R.L. (2011) Models for Quantifying Risks, Fourth Edition. Winsted, CT: ACTEX Publications, Inc. Chapters 3, 5-15 (excluding Sections 11.6 and 15.5), 16 (Section 16.1 only). 2. ACTEX MLC Study manual, Fall 2012 Edition by Johnny Li and Andrew Ng. Course objectives: After taking the math 419 course sequence, students will be able to apply mathematical principles to traditional insurance and annuities products. Students will be able to use methods of pricing and evaluating risk for these products. Students will be able to demonstrate life contingency and risk theory and apply the theory to insurance products and business. For math 419B, students will be able to analyze reserves for insurance benefits and annuity payments, both single life and multiple lives. Course Conduct: You are expected to attend each class. Homework will be due every Wednesday before the class starts. Homework questions are expected days before the due time. So Begin the Work Early! If you expect to do well in this course, you must do the homework. Limited time will be available during class to discuss the homework problems and your instructor is available during office hours and by appointment. Seeking help timely is important to succeed in our quarter setting. Your questions are always welcomed during class and outside the class. This is a highly challenging course demanding diligence and continual work on problems. Expect to spend hours of concentration on the text reading and problem attempting. Students with Disabilities: If you require accommodation based on a documented disability, have emergency medical information to share, or need special arrangements in case of emergency evacuation, please discuss the situation with me as soon as possible. Course Prerequisites: Actuarial Mathematics (I) is a formal prerequisite for this course. You must know the basic notations, concept, and rules for survival functions, mortality tables, mathematical survival models, life insurance and annuity contracts, contract premiums, under both continuous and discrete survival time variable schemes. You must also know the formulas for their interdependent relationships and some proofs by using your pre-requisite in probability theory and calculus. These skills are crucial. You must be able to manipulate algebraic expressions, powers, logarithms, derivatives, and integrals. You should be able to solve linear, quadratic, exponential, logarithmic and trigonometric equations. In addition to the exams, there will be a spreadsheet project for you to develop throughout the quarter. Your working knowledge of Excel spreadsheets is assumed. If you happen to never touch any spreadsheet in your life, you should check out a book to study or you can come to my office hour so that I can walk you through the process. It is possible to arrange a workshop on Friday afternoons. You can also sit in my statistics lab hour in Bouillon 103 Friday 9-9:50 when it s possible for me to assist you. Please do not disturb the lab but seat yourself and wait until I am available for your questions. Learner Outcomes: Upon successful completion of this course, the student will understand: the concept and calculation of benefit premiums;

2 how benefit reserves can be evaluated for a variety of products and assumptions; the concept of modified benefit reserves and its applications; the practice to incorporate expenses and general financial liabilities; analytical methods for constructing reserve valuations; the various interpretations of the universal life insurance; the implementation procedures for insurance and annuity pricing through spreadsheet applications. 2 Grading: Your course grade will be determined by the following: 1. Three 100-point in-class exams. You can drop the lowest exam score. So these exams will count for up to 200 points. 2. Weekly homework worth up to 60 points. 3. A complete spreadsheet project worth up to 40 points. 4. A comprehensive final exam worth up to 100 points. A perfect score on both of the above categories would result in a total of 400 points. Your course grade will be determined by the percentage p of these points you earn, according the following scale. 93 p A 74 p 76 C 90 p93 A- 70 p 74 C- 86 p 90 B+ 65 p 70 D+ 84 p <86 B 58 p 65 D 80 p84 B- p 58 F 76 p80 C+ Note: No makeup exams will be given. If you miss an exam, it will be the one you drop. You must take the final exam to pass the course. It is highly unlikely to curve the grade regardless how the entire class is doing, either too well or too poor. I would like to hold consistent standards across classes. Course outlines: Topic Days (One day is one-hour) I. Benefit Premiums 6 1. Fully Continuous Premiums 2. Fully Discrete Premiums 3. True m-thly Payment Premiums 4. Non-Level Premium Contracts 5. The Percentile Premium Contracts 6. Expenses II. Benefit Reserves 8 1. Fully Continuous Benefit Reserves 2. Other Formulas for Fully Continuous Benefit Reserves 3. Fully Discrete Benefit Reserves 4. Benefit Reserves on a Semi-continuous Basis 5. Benefit Reserves Based on True m-thly Benefit Premiums

3 6. Reserves for Contingent Payment Models with m-thly Benefit Premiums 7. Multi-State Model Representation 3 III. Analysis of Benefit Reserves 8 1. Benefit Reserves for General Insurances 2. Recursion Relations for Fully Discrete Benefit Reserves 3. Benefit Reserves at Fractional Durations 4. Incorporation of Expenses 5. Universal Life Insurance IV. Multiple Life Functions 5 1. Joint Distributions of Future Lifetimes 2. The Joint-Life Status 3. The Last-Survivor Status 4. More Probabilities and Expectations Dependent Lifetime Models-Common Shock (SPRING QUARTER) 6. Insurance and Annuity Benefits -Survival Statuses -Special Two-Life Annuities -Reversionary Annuities 7. Evaluation Special Mortality Assumptions -Gompertz and Makeham Laws -Uniform Distribution TESTING 3 TOTAL 30 Spreadsheet Project: You are required to develop a spreadsheet application that will implement the N.S.P. formula for a variety of life insurance and life annuity contracts introduced in math 419A. Single life contracts for this winter quarter and joint lives can be in spring quarter. You should use the illustrative life table (from the MLC exam) as a first attempt since this table provides the whole life cases for every integer age on the table, thus serves a nice verification vehicle for the formulas built in the cells. You will have to input formulas for term life, whole life, and deferred life and make the calculation results accessible to your program users. This is not an isolated project but connect to your grasps of computational and conceptual techniques associated with your learning. As an option, you can also program valuation dates at fractional age under various mortality assumptions (UDD, De Moivre, Constant Force,..etc) Over and above the intensive programming that you are involved, you are expected to come up with a theme topic (or "overarching question") to differentiate your spreadsheet projects from your peers. An ultimate goal of your project is to share how actuarial math works via life insurance business. The best part of student projects often lies on the learning experience and the creativity originated by you. You will receive good sense of achievement for your work well done. You are urged to present your finished project to SOURCE, a once-a-year campus event. My role would be mentoring and coaching you to handle errors or hurdles in formula comprehensions and coding. I expect it to be a significant time commitment but believe worthwhile to do. A possible project expansion for spring may be on the benefit reserves. You may use life tables your pick from the SOA, AAA websites or internet. I can assist you with formatting the text file into the.xls spreadsheet format. Any other ideas from you are welcome and encouraged!

4 4 Tentative Schedule (Any change will be announced in class.) Week Reading and Homework Assignment 0. 1/3-1/4 Chapter 9, Lecture 14 Exercises: Chapter 9, #1-8 (review these problems) #9-12, /7-1/11 Chapter 9 Lectures 15, 16 Exercises: Ch9 #15-23, /14-1/18 Exam 1 (Covers Chapter 9) on Friday! 3. 1/21-1/25 Chapter 10 Lecture 18 Exercises: Ch10 #1-12, /28-2/1 Lectures 19, 20 Exercises: Ch10 #19-24, /4-2/8 Exam 2 (Covers Chapter 10) on Friday! 6. 2/11-2/15 Chapter 11 Lecture 21 Exercises: Ch11 #1-4, 7-11, /18-2/22 Lectures 22, 23 (optional) 8. 2/25-3/1 Chapter 12 Lectures 1, 2, 3 (from Volume 2) Exercises: Ch12 #1-5, 6-10, /4-3/8 Exam 3 (Covers Chapter 11 to 12.4) on Thursday! Spreadsheet project due on Friday! 10. 3/11-3/15 FINAL EXAM WEEK

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