Courses

Probability is the foundation on which statistics is built. The purposes of this course are 1) to introduce you to probability and 2) prepare you to take a sequel course on statistical inference (Statistics 4204,5204).

We shall begin by covering the basic axioms of probability and using these in some simple settings. Then we will take up the idea of independence and conditional probability. Following we shall consider random variables, and the properties first of univariate discrete and continuous distributions. When we look at two or more variables, additional considerations arise, such as the relationship between the variables|conditional distributions and marginal distributions. Following these basics, we will then take up some ways of summarizing distributions, e.g., expectations and variances and, in summarizing relationships among variables, covariance and correlation. We then take up some of the more important distributions in statistics. In particular, for the discrete case, we will study the Bernoulli and binomial distributions and the generalization to the multinomial distribution, also the Poisson distribution. For continuous distributions, we take up the univariate and bivariate normal, the Gamma and the Beta distribution. In statistical applications, sums of independent random variables (for example, a sample average is such a sum, divided by sample size) are extremely important and characterizing the properties of these in large samples justifies many of the ways in which we make inferences in statistics. Thus, we take up the properties of these sums in large samples, focusing on stating laws of large numbers and also a simple central limit theorem.

The aim of the course is to describe the two aspects of statistics {estimation and inference {in some details. The topics will include maximum likelihood estimation, Bayesian inference, confidence intervals, bootstrap methods, some nonparametric tests, statistical hypothesis testing, linear regression models, ANOVA, etc.

This course explores actuarial models for life contingent risks, their theoretical basis and application.  It discusses survival models, life tables, life insurance and annuity benefits, premium and reserve calculations related to policies on a single life. 

This course covers the material of the long term portion of the Fundamentals of Actuarial Mathematics (FAM) exam of the Society of Actuaries (SOA).  This is a core course of the Actuarial Science program. Students who have already passed the MLC exam, the LTAM exam or the FAM exam (or its long term portion) administered by the SOA are exempted from this class and can substitute an elective

This course is a continuation of Actuarial Methods I. It discusses Markov chains and their application to a wide variety of long term insurance products, fundamentals of pension liabilities, profit tests, universal life, and equity-linked insurance. This class, along with Actuarial Methods I, covers the material of Exam LTAM of the Society of Actuaries. Students who have already taken and passed the ALTAM exam or the LTAM exam administered by the SOA are exempted from this class and can substitute an elective.

This course provides an introduction to the tools for pricing and reserving for short term insurance. We will discuss methods for calculating IBNR reserves, ratemaking, frequency and severity models used for modeling coverage modifications, statistical methods for fitting, evaluating, and selecting parametric models for frequency and severity, and three credibility methods.

This class covers the short-term material of Exam FAM and also covers the material of Exam ASTAM of the Society of Actuaries, and some of the material on Exams MAS I, MAS II, and 5 of the Casualty Actuarial Society. This is a core class of the Actuarial Science program. Students who have already taken and passed the FAM exam (or its short term portion) and the ASTAM exam administered by the SOA are exempted from this class and can substitute an elective.

This course discusses three extensions to the modeling methods discussed in the Predictive Modeling course:  ARIMA and ARCH/GARCH time series models, linear and generalized linear mixed models, and Bayesian methods for estimating linear and generalized linear models, including the use of Markov Chain Monte Carlo (MCMC) to estimate the posterior distribution.  In addition, the course briefly discusses various graphical techniques for evaluating insurance pricing models.

This class covers most of the material of Exam MAS II of the Casualty Actuarial Society. This is a core course of the Actuarial Science program. Students may take either this course or Advanced Actuarial Methods. Those who have already taken and passed the MAS II exam for CAS are exempted from this class and can substitute an elective.

Familiarity with linear and generalized linear models covered in Predictive Modeling in Finance and Insurance (PS5840) is helpful. Prior exposure to linear algebra, calculus, statistics, and a working knowledge of R and spreadsheets are necessary. Exposure to credibility concepts covered in Actuarial Models may also be useful.

This course introduces to the students, generalized linear models (GLM), time series models, and some popular statistical learning models such as decision trees models as well as random forests and boosting trees.  The aim for GLM is to provide a flexible framework for the analysis and model building using the likelihood techniques for almost any data type. The aim for the statistical learning models is to build and predict or understand data structure (if unsupervised) using statistical learning methods such as tree-based for supervised learning and the Principle Component Analysis and Clustering for unsupervised learning.  It develops a student’s knowledge of the theoretical basis in predictive modeling, computational implementation of the models and their application in finance and insurance. Tools such as cross-validation and techniques such as regularization and dimension reduction for fitting and selecting models are explored.  We also implement these models using a combination of Excel and R.

The class covers the material of Exams, Statistics for Risk Modeling (SRM) and Predictive Analytics (PA) of Society of Actuaries, and some material of Exams, Modern Actuarial Statistics I (MAS-I) and MAS II by the Casualty Actuarial Society. This is a core course for the Actuarial Science students. Students who have already taken and passed the SRM and PA exams administered by the SOA are exempted from this class and can substitute an elective.

This course explores machine learning models, their theoretical basis, computing implementation and applications in finance and insurance.  It discusses machine learning models for regression, classification and unsupervised learning;  tools such as cross validation and  techniques such as regularization, dimension reduction and ensemble learning;  and select algorithms for fitting machine learning models.  This course offers students an intensive hands-on experience where they combine theoretical understanding, domain knowledge and coding skills to better inform data-driven decision making.

Some topics covered are relevant to the statistical learning portion of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS) curricula, and the quantitative methods section of the Chartered Financial Analyst (CFA) Institute curriculum.  This is a core course of the Actuarial Science program.

Industry representatives conduct a series of noncredit seminar sessions designed to expose students to the actuarial profession as well as to address a range of topics in actuarial science.

This course will provide an overview of life insurance company structure, life insurance products, product development and pricing considerations, investments and the regulations and liabilities that drive life insurance company decisions. All life insurance actuaries must master the concepts of financial mathematics and how to apply those concepts to calculate projected present values and accumulated cash flows. You will study these concepts and apply them to calculate basic reserves, new business pricing, and profitability metrics. This will include exploring various types of product designs. Actuaries play an important part in development and interpretation of the various financial statements that insurance companies are required to provide to the public. The course will illustrate the content of the most important statements, exhibits, and schedules and provide a description of their purpose. Insurance cash flows are unique in that there are many uncertainties and those cash flows stretch out into the future over a considerable amount of time. This leads to another important aspect of actuarial science, which is risk analysis and risk management. This course will study how companies map risks and set aside capital to provide for the uncertainties above and beyond those provided for by standard reserves, including an introduction to evolving uses of predictive analytics and enterprise risk management by insurance companies.

Finally, the course will cover current evolving trends, e.g., the growth of online life insurance products and services.

This course develops an understanding of the fundamental concepts of financial mathematics, and how
those concepts are applied in calculating present and accumulated values for various streams of cash
flows as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment
income, capital budgeting, and valuing contingent cash flows. The candidate will also be given an
introduction to financial instruments, including derivatives, and the concept of no-arbitrage as it relates to
financial mathematics.

The Financial Mathematics Exam assumes a basic knowledge of calculus and an introductory knowledge
of probability.

The first half of this course introduces key financial markets including interest rates, equity, foreign exchange, mortgage, and some derivatives. It also discusses interactions of the Federal Reserve and the securities firms and their effects on the markets. The 2nd half introduces some key metrics used in managing insurance companies including earnings, regulatory/economic capital and embedded value. These metrics are discussed in the context of insurance risks, financial markets, and regulatory regimes. The 2nd half also provides an overview of the major actuarial/finance functions in a typical insurance company (i.e. Valuation, Pricing, Risk, etc.) and more importantly how they use these metrics to manage profitability and risk. The course is intended to provide students with a broader background when dealing with financial and insurance products.

This course also touches on many topics required for the upper level actuarial exams by the SOA and should help lay the conceptual foundation. These exams include Corporate Finance, ERM, Individual Life and Annuity pricing and risk management, Life Finance and Valuation, and Investment Risk Management.

This course is a workshop in ERISA and Taxation Rules for Actuaries. Actuarial science can be applied and cover a number of welfare benefit arrangements (such as life insurance, medical, disability, severance etc.), qualified plans and nonqualified deferred compensation plans. The services and products that are developed in the actuarial field may be governed by certain federal laws. In the U.S., these arrangements are governed by the Employee Retirement Income Security Act ("ERISA"). In addition, certain federal taxation and reporting rules may apply. To be successful in the field will require an understanding of these rules, reporting requirements, taxation rules and the government agencies (Internal Revenue Service, Department of Labor and Pension Benefit Guarantee Corporation) responsible for oversight of such arrangements. Other topics covered will include SEPs, Simple Plans, 403(b) plans, 457 plans and Nonqualified Deferred Compensation Plans.

The goal of this elective course is to provide you with a broad understanding of fixed income securities and how they are used for asset liability management (ALM) in financial institutes. This course is designed for individuals who currently work or plan to work as insurance and financial professionals such as actuaries, traders, and quants. The course builds on concepts introduced in several of the program’s core courses and emphasizes the application of theories. The course covers content adapted from the SOA syllabus for fellowship exams and is split into four parts: interest rate risk measurements, interest rate management—ALM strategy, ALM decision-based asset allocation, and value-based management. In this course, you will learn several ALM techniques related to mitigating interest rate risks, managing risk and return trade-offs, and setting strategic asset allocation (SAA) to achieve an optimized risk/return portfolio. Additionally, you will be introduced to the concepts of value-based management and economic value of liabilities. Completing this course will give you a fundamental basis for understanding ALM in financial organizations and further prepare you to apply these concepts in real-life situations under both generally accepted accounting principles (GAAP) and market consistent approaches.

This course introduces general principles of ratemaking and reserving as they relate to P&C insurance products. Students will learn actuarial conventions and terminology and structure insurance data accordingly. We will discuss techniques needed to restate historical premium and loss information at current levels and derive consistent profitability metrics. Advantages and disadvantages of various traditional pricing and reserving techniques will be discussed as well as classification of insureds and other important topics.

This course discusses topics in database navigation, select advanced predictive analytics models, and model interpretability. Topics include relational databases, generalized additive models, deep learning models, linear mixed models, Bayesian approaches, and interpretable machine learning. This course offers students an intensive hands-on experience where they combine theoretical understanding, domain knowledge and coding skills to better inform data-driven decision-making.

Topics covered are relevant to the Advanced Topics in Predictive Analytics (ATPA) exam of the Society of Actuaries.  Topics in deep learning are also relevant to the statistical learning portion of the Casualty Actuarial Society (CAS) curriculum, and the quantitative methods section of the Chartered Financial Analyst (CFA) Institute curriculum. 

This course will introduce students to major issues currently of concern to all investors. It can give you the skills to conduct a sophisticated assessment of current issues and debates covered by the popular media as well as more-specialized finance journals. These skills are essential for people who pursues a financial service career, especially in today’s rapidly evolving environment. The material presented in this course are both practical important and intellectually interesting.

This course is consistent with and relevant to Chartered Financial Analyst (CFA) curriculum. It covers all subjects in CFA test and most of problems are in the same format as the CFA examination questions. This course will also provide a foundation for further study in Financial Risk Management and Financial market related courses.

Risk Management becomes more and more important in the financial industry especially after the global financial crisis. Large financial institutions are facing high regulatory pressure from the government and public. In response to this pressure, risk management in the financial industry has been transformed dramatically over the past decade. Today, about 50 percent of the function’s staff are dedicated to risk-related operational processes such as credit administration, while 15 percent work in analytics. McKinsey research suggests that by 2025, these numbers will reach 25 and 40 percent, respectively.

This course is designed to provide students with a high-level overview of modern risk management. This is then followed by an in-depth examination of the techniques and management structures used to assess and control risk, including a detailed discussion on the implementation of Value-at-Risk, which is becoming the de facto standard for measuring risk across all the major classes: market, credit, liquidity and operational.

This course is consistent with and relevant to Financial Risk Manager (FRM) curriculum. It covers majority of FRM learning objectives in the test and it is deeper in the quantitative modelling and analysis.

Insurance company risk management practices and requirements have evolved significantly over the last ten years, with the advances in regulation (e.g., Solvency II, NAIC ORSA) and rating agency oversight. This elective course is designed for individuals interested in moving into risk analysis roles within property and casualty (P&C) insurance, also known as general insurance. It provides a practical review of leading quantitative risk assessment and analysis practices at P&C insurance companies. The course will give you a sound understanding of quantitative risk analysis principles that will help you expand your influence in your organization and improve the way you communicate about risk to regulators, rating agencies, and boards. The course focuses on current industry practices, critical analysis skills of risk, and the development and delivery of professional work products, to influence decision makers.

The course is divided into three parts:

• Introduction to P&C Insurance: you will review the unique characteristics of P&C insurers, including underwriting, claims, premiums, policy wordings, insurance law, and regulation;
• Risk Analysis: you will gain a deep understanding of the key principles underlying the implementation and application of risk management within an organization, including qualitative aspects such as framework, governance and processes, as well as quantitative methods of risk measurement and modeling; and
• Application: through a real life case study, you will work in a group to synthesize the quantitative risk analysis concepts with the realities of P&C insurance company information sources, develop and present a professional consulting work product to a real guest business leader from the insurance risk management community.

This course is a workshop in communication techniques and professional development. Students make presentations individually and in teams. Actuarial science can be complex and to be successful in the field will require effective communication skills to simplify and explain the complex.  The course covers communicating effectively, professional development, structuring presentations, delivery techniques and presentations.  The main objective for the course is to help students take the complex including business trends and communicate it in a manner that can be understood by the target audience. We will focus on improving communication skills, networking, interview skills, job opportunities and career development.   

This course covers how to generate reliable and sustainable incomes based on available resources and manage the key risks in retirement (or in the state of financial independence (FI)). We discuss the overall framework and the process and examine the major products and strategies used in practice, with a special focus on the areas related to actuarial science, such as the key insurance products (annuities, life insurance, and long-term care insurance) commonly used, how to position various investments in different types of accounts and withdraw in the most tax efficient manner to meet the income needs. Effective strategies to manage the top risks (longevity, inflation, sequence of return, liquidity, long-term care, and frailty) will also be covered.

This course is particularly applicable to students who are looking to develop their skills in a particular area of application of actuarial science. The course is delivered in a project format that will integrate specific elements of the curriculum into an applied project, giving students hands-on actuarial science application experience. Students may team up and undertake a special actuarial project and present as consultants or in house actuaries to a panel of actuaries who will grade the overall effectiveness of their approach, solution and communication. This course will help students increase their understanding of the real-world constraints under which actuaries operate. The course also serves the purpose of sharpening the students analytical and communication skills, by allowing them to apply their previous experience and knowledge gained from the program to real-world problems.

Review of elements of probability theory. Poisson processes. Renewal theory. Walds equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes

Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course

This course introduces the Bayesian paradigm for statistical inference. Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models; Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software. Prerequisites: A course in the theory of statistical inference, such as STAT GU4204 a course in statistical modeling and data analysis, such as STAT GU4205

The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.

Prerequisites: Pre-requisite for this course includes working knowledge in Statistics and Probability, data mining, statistical modeling and machine learning. Prior programming experience in R or Python is required. This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will be covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio of projects, and deeper understanding of several core statistical/machine-learning algorithms. Short project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications

Prerequisites: STAT GU4205 or the equivalent. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

Prerequisites: STAT GU4204 or the equivalent. STAT GU4205 is recommended. Modeling and inference for random processes, from natural sciences to finance and economics. ARMA, ARCH, GARCH and nonlinear models, parameter estimation, prediction and filtering. This is a core course in the MS program in mathematical finance.

Prerequisites: STAT GU4203. STAT GU4207 is recommended. Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations. Additional topics as time permits.

Prerequisites: STAT GU4264. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates. This is a core course in the MS program in mathematical finance.

Prerequisites: STAT GU4205 and at least one statistics course numbered between GU4221 and GU4261. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and non-standard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.

Data Visualization and Design

This elective is available to and highly recommended for students without a strong finance background. It introduces students to the fundamental financial issues of the modern corporation. By the end of this course, students will understand the basic concepts of financial planning, growth management, debt financing, equity valuation, and capital budgeting.  (This course is not automatically available for all students; students must contact their Advisor to determine eligibility to register.)

Availability

On Campus: Every term
Online: Every term

In this course, students will learn about financial derivative securities: their role in financial management is becoming increasingly important, especially in portfolio management. Students will work on assigned readings, class discussions and examinations .By the end of this course students will be able to:

• Identify valuation of various options and futures as well as their use in risk management. 

• Understand option and futures pricing models, option strategies and index arbitraging. 

• Evaluate common hedging problems and build synthetic derivative positions

In this course, students will learn fundamental marketing concepts and their application. Students will work extensively with case study projects. By the end of this class students will understand:

• The essential elements of a market and large-scale company strategy

• How to identify customers and competition

• The fundamental elements of the marketing mix (product, price, placement and promotion) 

• How to research consumer behavior and pricing strategies.

In this course, students will learn about the valuation of publicly traded equity securities through case study analyses, class discussion, independent exercises, reading assessments, group work, and  weekly deliverables, culminating in a final investor pitch. 

By the end of the semester students will be able to:

• Perform fundamental analysis ("bottoms-up," firm-level, business and financial analysis)

• Prepare pro forma financial statements, estimate free cash flows and apply valuation models.

• Understand the importance of reasoned analysis and critical thinking when evaluating firms.

Prerequisites: MATH UN1102 and MATH UN1201 , or their equivalents. Introduction to mathematical methods in pricing of options, futures and other derivative securities, risk management, portfolio management and investment strategies with an emphasis of both theoretical and practical aspects. Topics include: Arithmetic and Geometric Brownian ,motion processes, Black-Scholes partial differential equation, Black-Scholes option pricing formula, Ornstein-Uhlenbeck processes, volatility models, risk models, value-at-risk and conditional value-at-risk, portfolio construction and optimization methods.

Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Review of the basic numerical methods for partial differential equations, variational inequalities and free-boundary problems. Numerical methods for solving stochastic differential equations; random number generation, Monte Carlo techniques for evaluating path-integrals, numerical techniques for the valuation of American, path-dependent and barrier options.

Prerequisites: Knowledge of statistics basics and programming skills in any programming language. Surveys the field of quantitative investment strategies from a buy side perspective, through the eyes of portfolio managers, analysts and investors. Financial modeling there often involves avoiding complexity in favor of simplicity and practical compromise. All necessary material scattered in finance, computer science and statistics is combined into a project-based curriculum, which give students hands-on experience to solve real world problems in portfolio management. Students will work with market and historical data to develop and test trading and risk management strategies. Programming projects are required to complete this course.

This course covers programming with applications to finance. The applications may include such topics as yield curve building and calibration, short rate models, Libor market models, Monte Carlo simulation, valuation of financial instruments such as options, swaptions and variance swaps, and risk measurement and management, among others. Students will learn about the underlying theory, learn coding techniques, and get hands-on experience in implementing financial models and systems.

Prerequisites: comfortable with algebra, calculus, probability, statistics, and stochastic calculus. The course covers the fundamentals of fixed income portfolio management. Its goal is to help the students develop concepts and tools for valuation and hedging of fixed income securities within a fixed set of parameters. There will be an emphasis on understanding how an investment professional manages a portfolio given a budget and a set of limits.

Course covers modern statistical and physical methods of analysis and prediction of financial price data. Methods from statistics, physics and econometrics will be presented with the goal to create and analyze different quantitative investment models.

The course will cover practical issues such as: how to select an investment universe and instruments, derive long term risk/return forecasts, create tactical models, construct and implement an efficient portfolio, to take into account constraints and transaction costs, measure and manage portfolio risk, and analyze the performance of the total portfolio.

Non-Linear Option Pricing

Corequisites: STAT GR5204 and GR5205 or the equivalent. Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.

This course uses a combination of lectures and case studies to introduce students to the modern credit analytics. The objective for the course is to cover major analytic concepts, ideas with a focus on the underlying mathematics used in both credit risk management and credit valuation.  We will start from an empirical analysis of default probabilities (or PD), recovery rates and rating transitions. Then we will introduce the essential concepts of survival analysis as a scientific way to study default.  For credit portfolio we will study and compare different approaches such as CreditPortfolio View, CreditRisk+ as well as copula function approach. For valuation we will cover both single name and portfolio models.

Students will examine the generally accepted account principles (GAAP) underlying financial statements and their implementation in practice. The perspective and main focus of the course is from the users of the information contained in the statements, including investors, financial analysts, creditors, and management. By the end of this class, students will be able to construct a cash flow statement, balance sheet and decipher a 10K report.

Industry representatives conduct a series of noncredit seminar sessions designed to expose students to the actuarial profession as well as to address a range of topics in actuarial science.