An overview of methods and problems in the analysis of time series data related to finance and insurance. The course will focus on both theory and application with real datasets using R and Python and will require writing reports. Topics include stationary processes, linear processes; elements of inference in time and frequency domains with applications; ARMA, ARIMA, SARIMA, ARCH, GARCH; filtering and smoothing time-series; and State-space models.

This course provides an overview of the key statistical tools, methodologies, and algorithms used in life insurance and property and casualty insurance with a focus on numerical implementation and data applications. The life insurance component covers topics including stochastic mortality modelling and evaluation of (joint) life products via Markov Chains. The property and casualty component focuses on data driven rate making methods and stochastic pricing and reserving techniques.

This advanced course focuses on the design and implementation of machine learning methods and model risk management practices for financial and insurance applications. Topics include supervised learning (GLMs, survival models, decision trees, ensemble methods, and neural networks), unsupervised learning (PCA and clustering), and reinforcement learning. Students will also explore modern paradigms such as transformer architectures and large language models, including fine-tuning and prompt engineering.

The course emphasizes model development, refinement, and customization, oftentimes from first principles, across different stages of the data science lifecycle, building upon the data-preparation and workflow foundations established in Data Science and Machine Learning I. This course places a heavier emphasis on programming and applied implementation using modern data science libraries and tools.

This course features studies in the risks, and how to quantify and manage those risk, in financial and mortality linked insurance products. Topics include: hedging of guarantees embedded in equity-linked insurance and annuity products, asset-liability management, determination of regulatory and economic capitals, insurance securitization (life and P/C), longevity bonds and derivatives, reinsurance, catastrophe bonds and derivatives.

This course explores what are the various issues that arise when machine and statistical learning methods are used in practice on big data to inform business intelligence (in finance and insurance). In practice, data is not clean, number of features is large, feature engineering must be carried out, and data is often multi-modal consisting not only of structured data, but also of images, text, and social network data. In this course, students will be exposed to various techniques and practical know-how to deal with these cases and learn how to present results to practitioners who are not domain experts.

This course extends over the Fall/Winter semesters and will feature invited guest speakers delivering both academic and practical seminars on current aspects of finance and insurance modeling, pensions, valuation risk management, regulation, and accounting.

This course takes cases from a variety of problems in the financial and insurance worlds and students will work in groups to develop both the theory and implementation of cases, write reports, and deliver presentations on their findings. The course will be led by industry practitioners. Sample topics include: Solvency II, Pension Benefits Act, valuing and managing complex annuity riders.

In this course we will study techniques and algorithms for creating effective data visualizations based on principles from graphic design, visual art, perceptual psychology, and cognitive science.This course is targeted both towards students interested in using visualization in their own work, as well as students interested in building better visualization tools and systems.

Students will complete an industrial internship or research project and write a report, present, and defend it.

This course explores the practical application of various numerical methods to finance and insurance modeling. It covers topics including: the generation of random variables, simulating solutions of stochastic differential equations, variance reduction methods, multi-level sampling, least square Monte Carlo, Markov chain Monte Carlo, and solving partial difference equations stemming from derivative valuation, optimal control, and optimal stopping.

This course provides a rigorous and hands-on exploration of numerical techniques used to model complex systems in finance and insurance. Students will learn how to simulate and analyze stochastic processes that underlie asset prices, risk dynamics, and actuarial models.

Key topics include the generation of random variables, simulation of stochastic differential equations, and advanced Monte Carlo methods such as variance reduction, multilevel and importance sampling, least-squares Monte Carlo, and Markov chain Monte Carlo for Bayesian inference. Emphasis is placed on both the theoretical foundations and practical implementation of these methods in real-world financial and insurance contexts.

This course provides an introduction to a scholarly approach to teaching statistics in higher education. Emphasis is placed on the use of statistics education research, effective communication of fundamental statistical concepts typically encountered in introductory statistics, alignment of learning outcomes, course activities and assessments, recognition of common misconceptions and how to address them, and effective integration of educational and statistical technologies. No prior teaching experience is necessary.

This is a reading course primarily meant to sequentially follow a modular course offered in the Department. Its purpose is to offer further supervised study of an advanced topic covered for the ambitious student.

This is the Department's core graduate course in statistical theory. It covers the basic principles of statistical inference, their application to a variety of statistical models, and some generalizations to more complex settings.

This course will explore Monte Carlo computer algorithms, which use randomness to perform difficult high-dimensional computations. Different types of algorithms, theoretical issues, and practical applications will all be considered. Particular emphasis will be placed on Markov chain Monte Carlo (MCMC) methods. The course will involve a combination of methodological investigations, mathematical analysis, and computer programming.

This is a self-directed reading course. Please consult the department for eligibility and enrolment procedures.

This is a self-directed reading course. Please consult the department for eligibility and enrolment procedures.

This graduate course is changes from term-to-term depending on the topic and will be updated to reflect the special topics in terms when this course is offered.

This course will cover current topics in Data Science from a statistical perspective. The exact topics will vary from year to year. Emphasis will be on practical aspects of data science. This could include tools, workflows, reproducibility, and communication through a statistical lens but not all topics will be covered exhaustively every year.

This course explores advanced topics at the forefront of mathematical finance. Core themes include the theory and applications of forward-backward stochastic differential equations, stochastic optimal control, and the Hamilton-Jacobi-Bellman equation. Additional topics covered are the stochastic Pontryagin principle, finite player and mean field games, models driven by Lévy processes, and contemporary topics chosen by the instructor. Emphasis is placed on both the mathematical foundations and their relevance to modern problems in finance.

The problem of minimizing an expected value is ubiquitous in machine learning, from approximate Bayesian inference to acting optimally in a Markov decision process. Progress on this problem may drive advances in methods for generating novel images, unsupervised discovery of object relations, or continuous control. This course will introduce students to various methodological issues at stake in this problem and lead them in a discussion of its modern developments. Introductory topics may include stochastic gradient descent, gradient estimation, policy and value iteration, and variational inference. The class will have a major project component.

Functional data analysis (FDA) has received substantial attention in recent years, with applications arising from various disciplines, such as engineering, public health, finance, etc. In general, the FDA approaches focus on nonparametric underlying models that often assume the data are observed from realizations of stochastic processes with smooth trajectories. This course will cover general issues in functional data analysis, such as functional principal component analysis, functional regression models, curve clustering, and classification. An introduction to smoothing methods will also be included at the beginning of class to provide a basic view of nonparametric regression (kernel and spline types) and serve as the basis of FDA approaches. The course will involve some computing and data analysis using R or matlab.

This course will focus on convergence rates and other mathematical properties of Markov chains on both discrete and general state spaces. Specific methods to be covered will include coupling, minorization conditions, spectral analysis, and more. Applications will be made to card shuffling and to MCMC algorithms.

With the availability of high frequency financial data, new areas of research in stochastic modeling and stochastic control have opened up. This six-week course will introduce students to the basic concepts, questions, and methods that arise in this domain. We will begin with the classical market microstructure models, understand different theories of price formation and price discovery, identify different types of market participants, and then move on to reduced form models. Next, we will investigate some of the typical algorithmic trading strategies employed in industry for different asset classes. Finally, we will develop stochastic optimal control problems for solving optimal liquidation and high frequency market making problems and demonstrate how to solve those problems using the principles of dynamic programming leading to Hamilton-Jacobi-Bellman equations. Students will also have a chance to work with historical limit order book data, develop Monte Carlo simulations and gain a working knowledge of the models and methods. and methods.

Tentative topics include: Market Microstructure; Overview of Stochastic Calculus; Dynamic Programming & HJB -Dynamics of LOB-Optimal Liquidation; Market Making; Risk Measures.

The course will cover modeling, estimation and inference of non-stationary time series. In particular, we will deal with statistical inference of trends, quantile curves, time-varying spectra and functional linear models related to non-stationary time series. With the recent advances in various fields, a systematic account of non-stationary time series analysis is needed.

Inference based on the likelihood function has a prominent role in both theoretical and applied statistics. This course will introduce some of the more recent developments in likelihood-based inference, with an emphasis on adaptations developed for models with complex structure or large numbers of nuisance parameters. Special emphasis will be given to applications in biology and medicine throughout the course. Tentative topics to be covered include: review of likelihood inference and asymptotic results; adjustments to profile likelihood; misspecified models — composite likelihood; partially specified models — quasi-likelihood; properties and limitations of penalized likelihood.

The aim of this course is to provide an introduction to advanced insurance risk theory. This course covers frequent and severity models, aggregate losses, and compound distributions, EM algorithm, model selection, and estimation.

This course aims to discuss the latest research in insurance risk modelling in general insurance. It covers insurance data analysis, probababilty, and statistical models for insurance ratemaking and reserving, and their estimation procedures.

The general mathematics and logical foundations for statistical inference: geometric, algebraic, and topological symmetries that arise naturally in the solution to the inference problem, including rigorous comparison of the bayesian and frequentist approaches, and the group theoretic considerations of invariance (algebraic and logical symmetry), both on the sample space as well as on the parameter space (and both either implicit or manifest) that must be taken into account in the analysis. Unusual for the development, but fundamental to the inherent logic of such considerations, the finite-finite case is given special attention in respect of both sample space and parameter space.