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.

Availability

On Campus: Every term
Online: Not offered

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.

Availability

On Campus: Every term
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Not offered
Online: Spring

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.

Availability

On Campus: Not offered
Online: Fall

This course is designed to equip students in the Columbia Actuarial Program with the technical software skills essential for modern actuarial work, with a special focus on Casualty Actuarial Science. Through this course, students will gain proficiency in Excel and R—two foundational tools used in data analysis, reserving, ratemaking, and simulation modeling. Excel will be explored as a powerful and accessible tool for structuring actuarial models, performing sensitivity analysis, and managing large data sets. R will be taught as a robust statistical programming language that supports reproducible actuarial analysis, including the use of GLMs, bootstrapping methods, and data visualization. The course will also include an introductory segment on Python, highlighting its growing relevance in automating workflows, handling large-scale data, and integrating with machine learning frameworks that may be increasingly relevant in pricing and predictive modeling.

The broader aim of this course is to bridge the gap between theoretical actuarial concepts and practical implementation through programming. By learning these software tools, students will be able to operationalize core actuarial principles—such as risk modeling, claim development, and stochastic analysis—within real-world business contexts. The course aligns with the Actuarial Program’s mission to produce industry-ready professionals who can not only understand the mathematical underpinnings of risk but also communicate and deliver insights through modern analytics platforms. It supports the development of computational thinking, data fluency, and technical agility, which are increasingly critical in actuarial practice as the industry becomes more data-driven and technologically complex.

This is an elective course available exclusively to students enrolled in the Columbia Actuarial Program. No prior experience with Excel, R, or Python is required, making it an ideal entry point for students new to programming or applied analytics. The course will be conducted fully online over the course of a full academic semester, providing flexibility while maintaining rigorous engagement through weekly assignments, project-based learning, and applied actuarial case studies. Whether students aim to pursue traditional actuarial roles or explore emerging areas like InsurTech, this course will provide the software toolkit needed to succeed in a modern actuarial environment.

Availability

On Campus: Not offered
Online: Fall

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.

Availability

On Campus: Not offered
Online: Spring

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.

Availability

On Campus: Fall and Spring
Online: Not offered

This course discusses models of time series with constant variance, linear mixed models, Bayesian estimation of linear models and generalized linear models, Markov Chain Monte Carlo (MCMC) methods and linear model evaluation and selection. Some topics covered are relevant to the Modern Actuarial Statistics II (MAS-II) exam of the Casualty Actuarial Society (CAS). This is an elective course of the Actuarial Science program.

Availability

On Campus: Fall
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Fall and Spring
Online: Not offered

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.

Availability

On Campus: Fall
Online: Not offered

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.

Availability

On Campus: Fall
Online: Not offered

Communication skills are critical to the career trajectory of a risk professional. This workshop-style course develops the practical skills needed to communicate effectively with a diverse set of internal associates ranging from board members and executive officers to subject matter experts, as well as external stakeholders such as rating agencies and regulators. In this course, students learn techniques for effective listening and reading body language; creating and delivering professional presentations; leadership communication and persuasion; negotiation and conflict resolution; professional interactions and presence; and adapting to different communication styles. Through exercises, presentations, and case-based applications, students develop the ability to influence outcomes, achieve objectives, and build stronger professional relationships.

Availability

On Campus: Spring
Online: Not offered

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.

Availability

On Campus: Summer
Online: Not offered