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Financial Actuarial Mathematics Update: New Courses and 18-19 Schedule

Deadline: 
Saturday, June 1, 2019
Category: 
Contact: 
ugrad@math.ucla.edu

Dear Students, 

By now, you should be able to see when your Fall enrollment time begins in MyUCLA. The schedule of classes goes live on Monday, June 4th and priority pass will begin on Monday, June 18th. As a quick reminder, all upper division courses are restricted to math majors and minors only during the first pass. All remaining seats will be open to all majors once second pass begins and certain courses will be closed again during summer orientation (more information will be sent out later).

Following up on the last email to all students who are interested or continuing in the FAM major, here are the current updates on courses. The FAM major requirements (https://www.math.ucla.edu/ugrad/majors/fam) will remain the same: 12 lower division courses and 11 upper division courses. However, the actuarial courses have been restructured in part because of the changes to the exam syllabi posted by the SOA. Additionally, there are several new courses. These are listed below, and at the end of this message you will find instructions about fulfilling the requirements of the major with these new courses. In no case will the requirements be harder or will progress be delayed. If you have questions, please contact an adviser in the Undergraduate Office. 

The actuarial offerings for next year are: 

 

 

The actuarial courses for next year are: 

1.) Math 177 - Theory of Interest and Applications. A replacement of Math 175.

  • Description
  • Lecture, three hours; discussion, one hour. Requisite: course 32B. Types of interest, time value of money, annuities and similar contracts, loans, bonds, portfolios and general cash flows, rate of return, term structure of interest rates, duration, convexity and immunization, interest rate swaps, financial derivatives, forwards, futures, and options. Letter grading. 
  • Topics
    • Interest Rates and their Representation.
    • Annuities.
    • Loans and Bonds.
    • Rate of Return.
    • Term Structure of Interest Rates.
    • Duration and Immunization.
    • Interest Rate Swaps.
    • Introduction to Financial Derivatives.
    • Advanced problem analysis.
  • Objectives
    This is the first course with financial content of the FAM major. All later courses presume familiarity with many of the concepts introduced. Content includes numerous foundational concepts of financial mathematics, especially those from the theory of interest rates. Since one goal of the course is to help students prepare for the challenging exam FM (Financial Mathematics) of the Society of Actuaries, two classes before each midterm will be devoted to analysis of complex FM exam problems. While the basic ideas are mathematically elementary, their applications can be complex. The class is suitable for students who seek a career in financial engineering, the actuarial field, banking, etc., or who are seeking to improve their financial literacy in a highly quantitative way.
  • Learning Outcomes
    Student will be able to define concepts and solve problems of a type and difficulty similar to those on the SOA FM exam. The problems require using the following standard concepts of financial mathematics: interest rate, simple interest, compound interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate, convertible m-thly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value, annuity, annuity-immediate, annuity due, perpetuity, payable m-thly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity, loan, principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, bond, price, book value, amortization of premium, accumulation of discount, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, callable/non-callable, yield rate/rate of return, dollar-weighted rate of return, time-weighted rate of return, current value, duration (Macaulay and modified), convexity (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, stock price, stock dividend, cash flow matching, immunization (including full immunization), Redington immunization, swap rate, swap term or swap tenor, notional amount, market value of a swap, settlement dates, settlement period, counterparties, deferred swap, amortizing swap, accreting swap, interest rate swap, net payments, components of interest rates including: real risk-free rate, inflation rate, default risk premium, liquidity premium, and maturity risk premium, financial derivative, futures contract, forward contract, options, puts, calls. 
  • Examples of typical problems include:
    - calculating the market value, notional amount, spot rates or swap rate of an interest rate swap
    - constructing an investment portfolio to Redington (or otherwise) immunize a set of liability cash flows
    - calculating the duration (modified or Macaulay) and convexity of a cash flow
    - calculating the missing item, given any four of: term of loan, interest rate, payment amount, payment period, principal.

2.) Math 178A - Foundations of Actuarial Mathematics: Life Insurance and Annuities. Covers roughly Math 172B + first part of Math 172C.

  • Description
  • Lecture, three hours; discussion, one hour. Requisite: course 32B, 177, 170A or 170E or Statistics 100A. An introductory course on to the mathematics associated with long term insurance coverages. Single and multiple life survival models, annuities, premium calculations and policy values, reserves, pension plans and retirement benefits. Letter grading. 
  • Textbook
  • Dickson, David C.M., Hardy, Mary R. and Waters, Howard R., Actuarial Mathematics for Life Contingent Risks. 2nd ed., Cambridge University Press, 2013.
  • Topics
    • Life Insurance and Survival Models.
    • Life Tables and Selection.
    • Valuation of Insurance Benefits.
    • Variable Benefits.
    • Valuation of Annuities.
    • Premiums.
    • Policy Values.
  • Objectives
    This sequence is the actuarial core of the FAM major. 178A and the first half of 178B cover the syllabus of the SOA LTAM exam. By the end of 178A , students will be able to value and set premiums for insurance instruments of numerous types using traditional actuarial models. They will also understand the typical models of life contingencies which are used in the calculations
  • Learning Outcomes
    The student will understand: typical models for life insurance and annuities used to calculate their expected present values, premiums or contributions, and reserves.  For example, for premium calculations, the student will be able to calculate premiums based on the equivalence principle, the portfolio percentile premium principle, and profit testing, calculate probabilities, means, variances, and percentiles of random variables associated with a premium, and apply appropriate approximation methods such as uniform distribution of deaths, constant force, Woolhouse, and Euler.

    In terms of problem solving, the student will be able to solve problems of a type similar to those on the Society of Actuaries LTAM exam and which need only the portion of that syllabus covered by 178A

  • Weekly Syllabus
    • Week 1: Life insurance and survival models; Readings in DHW Chapter 1, Chapter 2, 2.2-2.3
    • Week 2: Survival models (cont.) and Life tables; Readings in DHW Chapter 2, 2.4-2.7, Chapter 3, 3.1-3.3
    • Week 3: Life tables and selection; Readings in DHW Chapter 3, 3.3-3.13
    • Week 4: Valuation of insurance benefits; Readings in DHW Chapter 4, 4.1-4.5
    • Week 5: Variable benefits; Readings in DHW Chapter 4, 4.6-4.8
    • Week 6: Valuation of Annuities; Readings in DHW Chapter 5, 5.1-5.10
    • Week 7: Valuation (end) and Premiums; Readings in DHW Chapter 5, 5.11-5.14, Chapter 6, 6.1-6.6.
    • Week 8: Premiums (continued), Policy Values, Readings in DHW Chapter 6, 6.7-6.10, Chapter 7, 7.1-7.3.1
    • Week 9: Policy Values (continued); Readings in DHW Chapter 7, 7.3-7.4
    • Week 10: Other topics; Readings in DHW Chapter 7, 7.5, 7.8-7.9

3.) Math 178B - Foundations of Actuarial Mathematics: Further topics in Long Term Actuarial Mathematics. Covers second half of Math 172C + first half of Math 173A.

  • Description
    Lecture, three hours; discussion, one hour. Requisite: course 32B, 177, 178A, 170B or 170S or Statistics 100B. Second part of the three quarter sequence Mathematics 178ABC. Multiple state models, pensions, profit testing, topics from statistics, esp. methods of estimation, and background material on probability distributions, especially those used in actuarial work. Letter grading. 
  • Textbook
  • A.) Dickson, David C.M., Hardy, Mary R. and Waters, Howard R, Actuarial Mathematics for Life Contingent Risks. 2nd ed., Cambridge University Press, 2013.
  • B.) Hardy, Mary R., Long-Term Actuarial Mathematics Study Note. Society of Actuaries, 2017. Education and Examination Committee of the Society of Actuaries - Long Term Actuarial Mathematics Supplementary Note.
  • https://www.soa.org/Files/Edu/2018/2018-ltam-supplementary-note.pdf
  • C.) Klugman, Stuart A., Panjer, Harry H., Willmot, Gordon E., Loss Models: From Data to Decisions. 4th ed., Wiley, 2012. 
  • Topics
    • Multiple State Models.
    • Long Term Coverages in Health Insurance.
    • Multiple State Models for Long Term Health and Disability Insurance.
    • Recursions for Policy Values with Multiple States.
    • Joint Life and Last Survivor Benefits.
    • Pension mathematics.
    • Emerging Costs for Traditional Life Insurance.
    • Basics distributional Quantities.
    • Characteristics of Actuarial Models.
    • Continuous Models.
    • Discrete Distribution.
  • Objectives
    The three quarter sequence 178ABC is the actuarial core of the FAM major. 178A and the first half of 178B give almost complete coverage the syllabus of the SOA LTAM exam. By the end of 178A, students are able to value and set premiums for insurance instruments of numerous types using traditional actuarial models. By the end of 178A, they will also understand the typical models of life contingencies which are used in the calculations. 178B first extends this work to multistate models, then covers pensions, health insurances, and profit-testing. The last three weeks of the course will focus on the probability distributions employed most commonly in actuarial theory. This begins the study of the Short Term Actuarial Mathematics syllabus.
  • Learning Outcomes
    Students will be able to work with parametric and non-parametric (multi-state) survival models including single life, multiple life, and multiple decrements, all in both continuous and discrete time. Students will be able to work with key examples from the health field (disability, long term care, critical illness, and long term care) insurance. Students will understand basic pension mathematics including their funding and the profit-testing of life insurance. Students will be able to work with parametric families of probability distributions used commonly for modeling severity, frequency and aggregate risk in the actuarial field, and their basic properties.

    In terms of problem solving, the students will be able to solve problems similar to those on the Society of Actuaries LTAM and STAM exams which is covered by a portion of that 178B. 

  • Weekly Syllabus
    • Week 1: Multiple State Models; Readings from DHW Chapter 8, 8.1-8.7
    • Week 2: Multiple Decrement Models; Readings from DHW Chapter 8, 8.8-8.13
    • Week 3: Further examples; Readings from 2018-ltam-supplementary-note(2).pdf, Section 2-4
    • Week 4: Joint life and last survivor benefits; Readings from DHW Chapter 9, 9.1-9.8
    • Week 5: Pension Mathematics; Readings from DHW Chapter 10, 10.1-10.6
    • Week 6: Pension Math and Midterm; Readings from DHW Chapter 10, 10.7
    • Week 7: Cash Flow Analysis for Life Insurance, Introduction to Tails; Readings from DHW Chapter 12, 12.1-12.8, KPW Chapter 3, 3.1-3.3 
    • Week 8: Tails and Measures of Risk; Readings from KPW Chapter3, 3.4-3.5, Chapter 4, 4.1-4.2
    • Week 9: Intro to Actuarial models; Readings from KPW Chapter 5, 5.1-5.4, Chapter 6, 6.1-6.3.
    • Week 10: Important Discrete Distributions; Readings from KPW Chapter 6, 6.4-6.6

4.) Math 178C - Foundations of Actuarial Mathematics: Loss models. Covers second half of Math 173A + Math 173B.

  • Description
    Lecture, three hours; discussion, one hour. Requisite: course 32B, 177, 178B, 170B or 170S or Statistics 100B. Third part of the three quarter sequence Mathematics 178ABC. Loss models associated with actuarial problems, severity, frequency, and aggregate loss models, parameter estimation (frequentist, Bayesian), model selection and credibility. Letter grading. 
  • Textbook
    A.) Klugman, Stuart A., Panjer, Harry H., Willmot, Gordon E., Loss Models: From Data to Decisions. 4th ed., Wiley, 2012.
    B.) Hardy, Mary R., Long-Term Actuarial Mathematics Study Note. Society of Actuaries, 2017. Education and Examination Committee of the Society of Actuaries - Long Term Actuarial Mathematics Supplementary Note.
    https://www.soa.org/Files/Edu/2018/2018-ltam-loss-models.pdf
    C.) Klugman, Stuart A., Panjer, Harry H., Willmot, Gordon E., Chapters 10–12 of Loss Models: From Data to Decisions. 5th ed., Society of Actuaries, 2018. Education and Examination Committee of the Society of Actuaries - Long-Term Actuarial Mathematics Study Note.
    https://www.soa.org/Files/Edu/2018/2018-ltam-loss-models.pdf
  • Topics
    • Frequency and Severity with Coverage Modifications.
    • Aggregate Loss Models.
    • Estimation Based on Empirical Data.
    • Frequentist Estimation.
    • Frequentist Estimation for Discrete Distribution.
    • Bayesian Estimation.
    • Model Selection.
    • Introduction and Limited Fluctuation Credibility.
    •  Greatest Accuracy Credibility.
  • Objectives
    The three quarter sequence 178ABC is the actuarial core of the FAM major. 178C covers topics associated with short term actuarial risk. With 178B, most of the topics 1-7 on the SOA STAM exam are covered.
  • Learning Outcomes
    Students will be able to analyse or construct: frequency and severity models with coverage modifications, aggregate loss models, with modifications, and their recursive construction, use maximum likelihood or Bayesian methods to estimate model parameters, estimate the variance of estimators, test hypotheses (using chi-square, Kolmogorov-Smirnov or likelihood ratio tests), estimate losses using credibility procedures (Bayesian, Buhlmann, and Buhlmann-Straub methods).

    In terms of problem solving, the students will be able to solve problems similar to those on the Society of Actuaries STAM exam and which is covered by a portion of 178C. With 178B, both courses will cover most of that syllabus. 

  • Weekly Syllabus
    • Week 1: Frequency and Severity models; Readings from KPW Chapter 8
    • Week 2: Aggregate loss models; Readings from KPW Chapter 9, 9.1-9.3
    • Week 3: Aggregate loss models (continued); Readings from KPW Chapter 9, 9.4-9.8
    • Week 4: Empirical estimation; Readings from SOA Handout 
    • Week 5: Empirical Estimation (continued); Readings from SOA Handout
    • Week 6: Midterm and Maximum Likelihood Estimation; Readings from KPW Chapter 13, 13.2
    • Week 7: Frequentist Estimation; Readings from KPW Chapter 13, 13.3-13.4, Chapter 14, 14.1-14.4, 14.6
    • Week 8: Bayesian Estimation; Readings from KPW Chapter 15, 15.1-15.3
    • Week 9: Model Selection; Readings from KPW Chapter 16, 16.1-16.5, 2018-stam-loss-models-data.pdf.
    • Week 10: Introduction to Credibility Theory; Readings from KPW Chapter 17, 17.1-17.5, Chapter 18, 18.4-18.6. 

Fulfilling Requirements for the FAM degree: 

All actuarial majors are required to finish a full actuarial sequence for the major. As for the three courses within "actuarial, economics or statistics", you still have the option of Econ 101-199, Stats 100C in addition to Math 156 (Machine Learning), Math 164 (Optimization) and Math 171 (Stochastic Process). Here is a road map for those who are about to begin the actuarial sequence or in the middle of the sequence:

 

For example, if a student has completed Math 172B or Math 173A, he/she should take Math 178B. If a student has not taken Math 172B or Math 173A (has not started any of the actuarial sequences), he/she should begin the new sequence - Math 178A. If a students has completed an actuarial sequence, Math 172BC or Math 173AB, then he/she has fulfilled that part of their major requirement. For those who are in the low GPA category, it is highly recommended that you email ugrad@math.ucla.edu or come in during drop in counseling to see what class you should exactly take since there are some content overlap. Options will vary and be on a case by case basis during this transition period.

As a quick reminder, we highly recommend actuarial students take the Math 170E and 170S route in lieu of Math 170A and 170B to ensure you learn some statistics which is crucial to the actuarial field.

5.) Math 170E - Introduction to Probability and Statistics: Part I Probability 

Lecture, four hours. Requisites: courses 31A and 31B. The Math 170E and 170S two quarter probability and statistics sequence is aimed to equip Math-Econ and Financial Actuarial majors with essential skills in these areas. Math 170E is an introduction to probability theory. Topics include discrete (binomial, Poisson, etc.) and continuous (Exponential, Gamma, Chi-square, normal) distributions, bivariate distributions, distributions of functions of random variables (including moment generating functions and Central Limit Theorem). Letter grading.

6.) Math 170S - Introduction to Probability and Statistics: Part II Statistics

Lecture, four hours. Requisites: courses 31A, 31B, and 170E. The Math 170E and 170S two quarter probability and statistics sequence is aimed to equip Math-Econ and Financial Actuarial majors with essential skills in these areas. Math 170S is an introduction to statistics. Topics include sampling; estimation and the properties of estimators; construction of confidence intervals and hypotheses testing. It is designed to meet the Society of Actuaries' VEE Requirements for Mathematical Statistics. Letter grading.

Further Courses: These are not currently required for the major but are meant to allow students to further their knowledge and/or make themselves more marketable.

7.) Math 179 - Topics in Financial Engineering

An optional course for students who want to learn more( beyond the content of 174E) about financial derivatives and risk management. It will also cover topics in finance such as mean-variance portfolio theory, Capital Asset Pricing model, etc. that are on the IFM exam but not in 174E. 

8.) Math 102 - Advanced Financial and Actuarial Problem Solving

An optional course to help students study for actuarial exams. Initially, 102’s will focus on exams P, FM, and IFM. 102 will be an active learning course, and one component will involve students presenting their work, with evaluation of presentation.

9.) Math 192 - Financial and Actuarial Practicum

An optional course for students who want to explore the different activities of actuaries and/or improve their soft skills (communication, writing, presentation, etc.). Outside speakers from the profession will come to present interesting topics in the field, including new areas. For the latter, topics mentioned have included self-driving cars and pet insurance. Some weeks, students will present. This will be offered first in Spring 2019. 

If you have any further questions, please email the office at ugrad@math.ucla.edu with your name, student ID number and specific question or come to drop in counseling (we are open throughout the summer).

UCLA Mathematics Department