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Course Descriptions

MET AT 601 Laboratory for Actuarial and Financial Data Analysis I

Prereq: Consent of instructor

The seminar intends to provide students with knowledge and skills to develop actuarial and financial database, and implement statistical modeling techniques as an integral part of automated data analysis. Real data will be used so that students may have opportunities to gain hands-on experience in assisting decision making related to actuarial field and financial market. Microsoft Access, especially Access Basic and DLL (Dynamic Link Library), as well as SAS will be used as major computer tools. Offered in the Fall semester. 2cr

MET AT 602 Laboratory for Actuarial and Financial Data Analysis II

Same as MET AT 601, offered in the Spring semester. 2 cr

MET AT721 Mathematics of Compound Interest

Prerequisites: MA225 (Multivariate Calculus)

This course develops uses of interest as it relates to the theory of finance. It will develop an understanding of interest calculations as they relate to bonds, mortgages, annuities under continuous and discrete payment schemes, and for instruments with non-level payment schemes. 4 credits.

MET AT722 Finance for Actuaries

Prerequisites: MET AT721 (Mathematics of Compound Interest)

This course covers basic models and tools of corporate finance. Topics include net present value valuation, internal rate of return and profitability index models, capital budgeting models and efficient market hypotheses. These tools will be used to understand and apply basic principles of option pricing theory, including the Black-Scholes formula with application to binomial lattice valuation. 4 credits.

MET AT731 Actuarial Mathematics I

Prerequisites: MA225 (Multivariate Calculus), MA581 (Probability), and AT721 (Mathematics of Compound Interest)

This course covers the fundamental principals of actuarial science. It begins with a discussion of survival models, including the functions that define them and special cases. A comparison is made between discrete and continuous models. Topics in the actuarial aspects of insurance will be covered, as will determination of annuities. Finally, the course will discuss the methodology of calculation of premiums. For all these topics, a basic framework will be presented, then more sophisticated models will be developed. 4 credits

MET AT732 – Actuarial Mathematics II

Prerequisite: AT731 or consent of instructor

This course builds on the topics developed in AT731. Insurance Reserves are introduced, and methods for determining reserves are studied. The course covers multiple life functions and multiple decrement functions. The latter part of the course focuses on ruin models. 4 credits

MET AT741 Actuarial Statistics I

Prerequisite: MA582 (Mathematical Statistics).

This course covers distributions of the size and frequency of insurance claims. Topics include empirical estimation, parametric estimation, Bayesian estimation, models for incomplete data, and evaluation of estimation processes. It also includes modeling problems arise from truncation and modification at zero, compound frequency, as well as the interaction of frequency with severity and exposure. The course emphasizes applications of statistical principles in actuarial models and modeling. 4 credits

MET AT742 Actuarial Statistics II

Prerequisite: AT741 (Actuarial Statistics I)

This course covers compound model for aggregate claims, credibility theory including Buhlmann-Straub credibility model and empirical Baysian methods. Also included are process models for insurance, discrete, finite-time ruin probabilities. The course emphasizes applications of statistical principles in actuarial models and modeling. 4 credits

MET MA743 Regression and Time Series

Prerequisite: MA582 (Mathematical Statistics) or consent of instructor

Part I of this course will cover simple and multiple regressions, serial correlation and heteroscedasticity, analysis of residuals, and stepwise analysis techniques. Part II will cover time series analysis including smoothing and extrapolation of time series, linear time series models, model building procedure, forecasting as well as case studies. 4 credits

MET AT744 Survival Analysis

Prerequisite: MA582 (Mathematical Statistics)

This course covers basic concepts and models in survival analysis, censoring and truncation, parametric and nonparametric estimation of the survival and cumulative hazards functions both for censored and truncated data, topics including excess mortality and Bayesian nonparametric methods, proportional hazards regression models, and hypothesis testing related to survival data. 4 credits

MET AT751 Individual Insurance Applications of Actuarial Principles

Prerequisite: AT731 or consent of instructor

This course covers the application of basic actuarial principles to individual life and annuity financial security systems. Material covered will include the purpose of these systems, the development of financial security products, risk classification, actuarial pricing assumptions, the calculation of product cash flows, the purpose of reserves and different reserve methods. Taxation, required capital, profit measurement, and reinsurance considerations for these products will also be studied. 4 credits

MET AT752 Group Insurance Applications of Actuarial Principles

Prerequisite: AT731 or consent of instructor

This course covers the application of basic actuarial principles to group life and group health financial security systems. Material covered will include the purpose of these systems, financial security product design and development, underwriting and risk management, premium determination, and the funding and valuation of group life and group health financial security systems. Group systems in the United States will be emphasized but the course will also review the Canadian health system. 4 credits

MET AT761 Mathematics for Investment and Portfolio Theory

Prerequisites: MA225 (Multivariate Calculus), MA581 (Probability), and AT721 (Mathematics of Compound Interest)

This course covers the risk and return characteristics of primary financial products, fundamental principles of modern portfolio theory, term structures and yield curves, Markowitz Portfolio Selection Model, CAPM and its applications to portfolio management, derivative securities, duration, immunization, and interest rate risk management. 4 credits

MET AT 762 Mathematical Finance

Prereq: MA 583 (Introduction to Stochastic Processes), and AT 761 (Mathematics for Investment and Portfolio Theory) or MA572 (Introduction to Mathematical Finance)

This course covers and emphasizes mathematical analysis of derivative products and the portfolio theory including Markowitz model, CAPM, and arbitrage pricing theory. 4 credits

MET AT782 – Pension Mathematics and Mortality Tables

Prerequisites: MA225 (Multivariate Calculus), MA581 (Probability), and AT721 (Mathematics of Compound Interest)

This course covers pension actuarial funding methods and the use of life contingencies. Included are analyses of the funding methods allowable under ERISA, their computation, and uses. We will also review the use of mortality tables, and discuss the various actuarial functions that are used in pension actuarial calculations. Finally, the course will review implications for pension funding under the IRS Code. 4 credits

MET MA 301 Calculus for Actuaries

Thorough reviews of calculus essential to actuaries and financial analysts. It includes differential and integral calculus; partial derivatives and multiple integration; differential equations; sequences and series; and applications in statistics, insurance, pension, and finance. 4 cr.

MET MA 603 SAS with Statistical Applications

Prereq: CAS CS 111, MET CS 201 or equivalent, and MET MA 214 (Statistical Methods II)

The course offers a unified and in-depth coverage of the statistical computer package SAS, and its statistical applications. Topics include the language of SAS, data formatting, creating and storing SAS data sets, file manipulations, macro procedure, and graphics. Also included are procedures for statistical techniques selected from analysis of variance, regression, factor analysis, scoring, and categorical data analysis. Several large data sets will be used as case study emphasizing hands-on experience with SAS for Windows. Laboratory course. 4cr

Actuarial Internship

MET AT981 Internship in Actuarial Science I

Prerequisites: Successfully completed MET AT722 and AT731, and maintain an overall cumulative GPA of 3.3 or higher.

The course is offered to students who seek for practical applications of actuarial principles in insurance companies, financial institutions, pension consulting firms, and other related fields. The course requires students to participate in an internship program with industry. Students need to submit monthly progress reports and a final semester report to the Chairman, Department of Actuarial Science at Boston University. Variable credits

MET AT982 Internship in Actuarial Science II

Prerequisites: Successfully completed MET AT722 and AT731, and maintain an overall cumulative GPA of 3.3 or higher.

Seminar and Directed Study

MET AT990 Seminar in Actuarial Science

Seminars are offered for special topics related to actuarial science, life insurance, casualty insurance, insurance medicine, mortality and mobility, health outcomes, economics, and policy, pension, social insurance, mathematical finance, statistics, and other related fields. Variable credits

MET AT991 Directed Study I

Prerequisites: consent of instructor

The course is offered to students who plan to engage in special research topics under the supervision of a faculty advisor. Application is made through the Department of Actuarial Science. Variable credits

MET AT992 Directed Study II

Prerequisites: consent of instructor

Preparation Courses for SOA/CAS Professional Actuarial Examinations

The following preparation courses are offered for students and the working actuarial professionals who plan for the SOA/CAS examinations. These are short-term intensive courses that cover topics related to the professional examinations in the most recent catalogs of SOA and CAS.

MET AT651 Mathematical Foundations of Actuarial Science. 2 credits

MET AT652 Interest Theory, Economics, and Finance. 2 credits

MET AT653 Actuarial Models. 2 credits

MET AT654 Actuarial Modeling. 2 credits

MET AT655 Applications of Basic Actuarial Principles. 2 credits

MET AT656 Finance and Investments. 2 credits

Courses offered jointly with Department of Mathematics and Statistics (Divided in to three categories: Probability and Statistics, Mathematical Finance, and Other Related Mathematics Courses)

Probability and Statistics:

CAS/MET MA 381 Elementary Probability

Prereq: MA 225 or MA 230

A calculus-based introductory course in probability. Language of probability, combinatorics, conditional probability, discrete and continuous random variables, the Poisson process, joint probability distribution, moment generating function, law of large numbers and central limit theorem, sample estimators for mean and variance. Cannot be taken for credit in addition to CAS MA 581. 4 credits

CAS/MET MA 416 Intermediate Statistical Methods

Prereq: MA 116 or MA 214 or equivalent. Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random-effect models. Trend analysis for repeated measures, expected mean squares, and nonparametric techniques. SAS is used throughout the course. 4 credits

CAS/MET MA 570 Stochastic Methods of Operations Research

Prereq: MA 225 or MA 230 and MA242 or MA 442.

Poisson processes, Markov chains, queuing theory. Matrix differential equations, differential-difference equations, probability-generating functions, single- and multiple-channel queues, steady-state and transient distributions. 4 credits

CAS/MET MA 575 Applied Regression and Analysis of Variance I

Prereq: MA 214, and MA 242 or MA 442, or MA 582, or consent of instructor.

General linear model, generalized inverse, quadratic forms and their distributions, least-square estimation, estimable function, Gauss-Markov Theorem, confidence region, test of linear hypothesis, and prediction. 4 credits

CAS/MET MA 576 Applied Regression and Analysis of Variance II

Prereq: CAS MA 575 or consent of instructor.

Analysis of variance, analysis of repeated measures, random-effect models, regression with random coefficients, multivariate models, two-stage linear models, and generalized estimating equations. 4 credits

CAS/MET MA 578 Bayesian Statistics

Prereq: MA 581 and MA 582.

The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration, and Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection. 4 credits

CAS/MET MA 581 Probability

Prereq: MA 225 or MA 230 or consent of instructor.

Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to MA 381. 4 credits

CAS/MET MA 582 Mathematical Statistics

Prereq: MA 381 or MA 581.

Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Also includes maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test. 4 credits

CAS/MET MA 583 Introduction to Stochastic Processes

Prereq: MA 381 or MA 581 or consent of instructor.

Basic concepts and techniques of stochastic processes as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability. 4 credits

CAS/MET MA 584 Survival Analysis--Statistical Methods for Lifetime Data

Prereq: MA 381 or MA 581 or consent of instructor.

Life tables, hazard plottings, types of censoring, and nonparametric methods; inference procedures for exponential, Weibull, and other distributions; proportional hazards and related regression methods; and competing risk models. 4 credits

CAS/MET MA 587 Sampling Design: Theory and Methods

Prereq: MA 582, or equivalent, and consent of instructor.

Stratified, cluster, systematic, multistage, double, and inverse sampling; optimum sample size, relative efficiency, sampling with unequal probabilities, and types of estimators (ratio and regression) and their properties. Measurement error nonresponse and randomized response models. 4 credits

CAS/MET MA 588 Nonparametric Statistics

Prereq: MA 582, or equivalent, and consent of instructor.

Theory and logic in the development of nonparametric techniques, including order statistics, tests based on runs, goodness-of-fit, rank-order (for location and scale), measures of association, analysis of variance, and asymptotic relative efficiency. 4 credits

CAS/MET MA 591 Introduction to Sequential Analysis

Prereq: MA 582 or consent of instructor.

Sequential probability ratio test (SPRT), operation characteristics function (OC) and average sample number (ASN), Wald's identity, truncated SPRT. Sequential tests for composite hypotheses, sequential estimation, sequential allocation and selection problems. 4 credits

CAS/MET MA 684 Multivariate Analysis

Prereq: one year of statistics.

Multivariate data, analytic techniques, multiple regression and correlation, factor analysis, discriminant analysis, cluster analysis, multidimensional scaling technique, and multivariate tests for one-, two-, and K-sample problems. 4 credits

CAS/MET MA 685 Advanced Topics in Applied Statistical Analysis

Prereq: MA 684 or consent of instructor.

Continues topics of MA 684 at a more advanced level. Canonical correlation, multivariate analysis of variance, and multivariate regressions. Categorical dependent variables techniques; discriminant analysis, logistic regression, and log-linear analysis. Factor analysis; principal-axes, rotations, and factor

scores. Cluster analysis. Power analysis. Extensive use of statistical software. 4 credits

GRS/MET MA 750 Methods of Statistical Modeling

Prereq: MA 582 and MA 684 or consent of

instructor (CAS MA 575 recommended).

Parametric models for a single response with

multiple predictors. Generalized linear models

(GLIM), inference for GLIM, model selection,

diagnostics. Logistic and probit regression,

log-linear models, Gamma and Poisson models,

survival models. Introduction to neural network

models. 4 credits

GRS/MET MA 751 Methods of Statistical Modeling

Prereq: MA 750 or consent of instructor.

Nonparametric modeling techniques such as

kernel, nearest neighbor, local regression

smoothers, and spline smoothers. Bias/variance

trade-off and selection of smoothing parameter.

Additive models, CART, MARS, and projection

pursuit regression techniques. 4 credits

GRS/MET MA 785 Time Series Modeling and

Forecasting

Prereq: MA 575. Autoregressive and

moving average processes, nonstationary

processes, mixed processes, seasonal processes,

autocorrelation and partial auto-correlation

functions, identification of models, estimation of

parameters, diagnostic checking of fitted models,

forecasting and updating, and other time series

approaches including regression and spectral

analysis. 4 credits

Mathematical Finance:

CAS/MET MA 502 Fundamentals of Finance

Prereq: MA 225 or MA 230 and MA 242

or MA 442. Time value of money, valuation of

assets, risk management and portfolio theory,

elementary methods for pricing of derivatives

and contingent claims, corporate financial

management. Reitano. 4 credits

CAS/MET MA 572 Introduction to

Mathematical Finance

Prereq: MA 226 or MA 231 and MA

381. A rigorous mathematical introduction to

developments in the field of finance.

Mathematics of modern portfolio theory,

capital asset pricing model, and arbitrage

pricing theory. Derivation of pricing models

for options, futures, and swaps based on

concepts from Itô calculus. 4 credits

CAS/MET MA 594 Stochastic Optimal Control

and Investment

Prereq: MA 225, MA 226, and MA

242. Sample topics: Brownian motion, Ito's

lemma, computer simulation, dynamic

programming, Bellmann's equation,

contingent claims analysis, investment

opportunities/timing, project/investment

valuation, dynamic equilibrium, sequential

investment. 4 credits

GRS/MET MA 795 Stochastic Methods of

Mathematical Finance

Prereq: MA 225, MA 511 and MA 581.

The essentials in stochastic calculus; Weiner's

process, martingales, stochastic integrals, Ito's

lemma, Girsanov's transformation formula,

diffusion processes. Most of the theory is

motivated with examples from finance and