**Graduate Studies and Postdoctoral Affairs (GSPA)**

Needles Hall, second floor, room 2201

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For more detailed course information, click on a course title below.

Course ID: 013389

Time value of money; simple and compound interest and discount; real returns; equations of value; loan schedules; valuation of fixed coupon bonds; valuation of real return bonds; term structure of interest rates; no arbitrage pricing; valuation of forward contracts; valuation of interest rate swaps. Duration and Immunization

Course ID: 013390

Models for future lifetime; insurance and annuity functions; life tables and their use; future loss random variable for a contract; calculations of premiums and reserves; standard international actuarial notation.

Course ID: 013391

Discrete and continuous random variables; generating functions; dependence; maximum likelihood estimation, functions of random variables; confidence intervals, hypothesis tests; Bayesian estimation, simple linear regression.

Course ID: 013392

Principles of financial accounting; construction and analysis of accounts. Sustainability reporting. Financial planning; capital budgeting, assessment of capital projects; long term financing; short term finance and planning

Course ID: 013393

Micro: Supply and demand; utility theory and risk aversion; production choices; competition; Macro: Fiscal and monetary policy; exchange rates; factors affecting inflation, unemployment, exchange rates and economic growth; introductory game theory; introduction to insurance economics.

Course ID: 013406

Mean-Variance portfolio theory; utility based portfolio theory; Capital-Asset Pricing Method, Arbitrage Pricing Theory, Efficient Markets Hypotheses; Capital structure and dividend policy; introduction to options with applications in corporate finance. Behavioural finance.

Course ID: 013395

Multiple state models; premiums and reserves for stat dependent policies, including joint life and last survivor benefits; cashflow projection methods; post retirement benefits: valuation and funding. Estimation and inference for survival models. Introduction to longevity models.

Course ID: 013396

Generalized linear models: multiple linear regression and normal linear model; exponential family; link functions; linear predicators; estimation; testing. Time series: Univariate ARIMA; multivariate AR; ARCH and other non-linear models.

Course ID: 013397

Counting processes; Markov processes and Kolmogorov equations; Brownian motion and geometric Brownian motion; Ito's lemma Monte Carlo simulation.

Course ID: 013398

Frequency and severity models; compound distributions, calculation of moments and probabilities using recursion; Bayesian estimation and credibility; claims reserving for non-life insurance using run-off triangle methods, introductory ruin theory.

Course ID: 013399

Binomial and lattice models for option pricing. Black-Scholes option pricing. Hedging option greeks. Exotic options. Term structure models including Vasicek, Cox-Ingersoll-Ross, Hull-White, Black-Derman-Toy. Interest rate options.

Course ID: 013400

This course provides a comprehensive treatment of various techniques from statistics, predictive analytics and machine learning that can be used to analyze data sets relevant for actuarial applications. Specific topics covered include: modeling principles and practice, analysis and estimation of survival models, insurance pricing using generalized linear models, classification and tree-based methods.

Course ID: 013401

This course considers actuarial risk management in the context of practical applications in life and non-life insurance, and in pensions. Topics covered include the role of the actuary; methods for pricing and reserving in life and non-life insurance; regulatory capital; risk transfer through reinsurance or securitization; product development; model risk and governance; pension risk management; embedded options in life insurance.

Course ID: 013402

This course combines enterprise and quantitative risk management to provide a comprehensive coverage of risk management science with applications in finance, insurance and corporate governance. Topics covered include: risk taxonomy; risk measures; extreme value theory; copulas; stress and scenario testing; interest rate risk management, credit risk management; regulation, including Basel, Basel 3 and Solvency 2; risk adjusted return; capital allocation.

Course ID: 013403

Elements of writing. Written project on an advanced topic, with a communications focus. Presentations: preparation and delivery.

Course ID: 000073

The Mathematics of Survival Models, some examples of parametric survival models. Tabular survival models, estimates from complete and incomplete data samples. Parametric survival models, determining the optimal parameters. Maximum likelihood estimators, derivation and properties. Product limit estimators, Kaplan-Meier and Nelson Aalen. Practical aspects.

Course ID: 010064

This course introduces enterprise risk management, with a focus on quantitative analysis and economic capital. Risk classification is first discussed with an emphasis on the types of risk most suited to quantitative methods. Risk measures, such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE or TVaR), are then introduced, and their use by firms and regulators to determine risk capital requirements is further highlighted. Different approaches are considered for developing loss distributions, including frequency/severity analysis and extreme value theory. Copulas and economic scenario generators are used to aggregate dependent risks. Different strategies for mitigating or transferring risk are reviewed. Additional topics that may be covered include credit risk, capital allocation and regulation of financial institutions.

Course ID: 011270

This course covers mathematical techniques for no-arbitrage pricing and hedging financial derivatives. Topics to be covered can be classified into three broad ares: derivatives markets (options; forwards and futures; other derivatives; put-call parity), discrete-time financial models (binomial models; general multi-period models; fundamental theorems of asset pricing; risk-neutral probability), and continuous-time financial models (basic stochastic calculus and Ito's lemma; Black-Scholes model; interest rate models and bond pricing).

Course ID: 000078

Cash flow projection methods for pricing, reserving and profit testing, deterministic, stochastic and stress testing; pricing and risk management of embedded options in insurance products; mortality and maturity guarantees for equity-linked life insurance.

Course ID: 015699

This course is designed to develop students' oral and written communication skills, using examples from actuarial risk management. It includes elements of writing, and also reading and summarizing leading edge work in actuarial theory and practice. Presentations and collaborative work are used to develop essential communication skills in both academic and professional contexts.

Course ID: 015988

This course acts as a capstone on the coursework based part of the PhD program and as a stepping stone to the PhD proposal and to research. It is aimed at developing research skills: critically reading published research, summarizing and synthesizing areas of research, writing and orally presenting summaries of research problems, data sets and theoretical and applied results. The course is designed to be integrative across core areas of the student discipline.

Course ID: 000082

Macro methods of runoff analysis: chain-ladder, least squares, separation, payment per claim incurred. Stochastic methods: Reid's method, see-saw, payment per unit of risk, autoregressive models, Kalman filter.

Course ID: 015701

This course presents advanced mathematical and computational tools useful to study loss frequency and severity models, and also aggregate claims models. Analytic and recursive evaluation of compound distributions are discussed, as well as generalized linear models for frequency and severity models. Other topics covered include pricing and insurance risk processes.

Course ID: 011274

The analysis of the development over time of the surplus on a portfolio of insurance business is considered. The classical Poisson and Sparre Andersen risk models are studied. Unified treatment of moments and distributions of quantities related to the event of ruin is done through a discounted penalty function approach. Random variables of interest include the time of ruin itself, the deficit immediately after ruin occurs, and the surplus immediately prior to ruin. Defective renewal equations and Laplace transforms are utilized extensively. Prerequisites are familiarity with aggregate loss models at the level of ActSc 431/831 or equivalent.

Course ID: 011275

Fundamental concepts in quantitative risk management. Topics typically include: risk measures, extreme value theory, multivariate distributions and copulas. This course has a focus on mathematical and statistical techniques. Other topics may be covered at the discretion of the instructor.

Course ID: 011276

Ruin Theory for heavy-tailed distributions. Fluctuation of maxima and upper order statistics. Extreme value distributions: Weibull, Frechet, Gumbel and generalized Pareto. Mean excess function. Statistical methods for external events. Estimation of parameters of extreme value and excess distributions. Applications in finance and insurance.

Course ID: 011686

Mixed Poisson and nonhomogeneous birth processes for claim counts; analytic, recursive, asymptotic and approximate evaluation of compound distributions for aggregate claims; reliability concepts and analysis of stop-loss moments; applications for inflation, incurred but not reported claims, and infinite server queues. Prerequisites are familiarity with aggregate loss models at the level of ActSc 431/831 or equivalent.

Course ID: 000044

The course introduces options and other derivative securities in different asset classes. The main focus is on methods of pricing in a multi-period setting, but continuous-time models are also discussed. Topics may include no-arbitrage pricing theory, the fundamental theory of asset pricing, complete and incomplete markets,and pricing of complex financial instruments.

Course ID: 000045

The course discusses methods and tools for modeling of financial derivatives in the continuous-time setting. Both theory and practical applications are discussed. The first part covers methods of pricing and hedging of derivatives under different assumptions about the dynamics of the underlying economic factors. Topics normally include currency derivatives, American and exotic options, futures contracts, stochastic volatility models and mean-variance hedging. The second part deals with modeling and pricing of interest-rate products. Topics may include short interest rate models, the Heath-Jarrow-Morton Framework, and Libor and swap market models.

Course ID: 000046

The course will cover selected and advanced topics in quantitative finance and risk management, with a particular focus on current developments. Topics may include robust and Bayesian portfolio optimization, limits to arbitrage, derivatives pricing under model uncertainty, credit risk models, and models of systematic risk.

Course ID: 011622

Basic optimization: quadratic minimization subject to leanear equality constraints. Effecient portfolios: the efficient frontier, the capital market line, Sharpe ratios and threshold returns. Practical portfolio optimization: short sales restrictions target portfolios, transactions costs. Quadratic programming theory. Special purpose quadratic programming algorithms for portfolio optimization: today's large investment firms expect to solve problems with at least 1000 assets, transactions costs and various side constraints in just a few minutes of computation time. This requires very specialized QP algorithms. An overview of such algorithms will be presented with computational results from commercial problems. The efficient frontier, the capital market line, Sharpe ratios and threshold returns in practice.

Course ID: 014063

The focus of this course is on the statistical modelling, estimation and inference and forecasting of nonlinear financial time series, with a special emphasis on volatility and correlation of asset prices and returns. Topics to be covered normally include: review on distribution and dynamic behaviour of financial time series, univariate and multivariate GARCH processes, long-memory time-series processes, stochastic volatility models, modelling of extreme values, copulas, realized volatility and correlation modelling for ultra high frequency data and continuous time models.

Needles Hall, second floor, room 2201

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.