# ACTSC Courses

# ACTSC 221 – Introductory Financial Mathematics (Non-Specialist Level)

The theory of rates of interest and discount; annuities and sinking funds with practical applications to mortgage and bond questions. Yield rates. [Offered: F,W,S]

# ACTSC 231 – Introductory Financial Mathematics

The theory of rates of interest and discount including the theoretical continuous case of forces of interest and discount. Annuities and sinking funds, including the continuous case. Practical and theoretical applications primarily to mortgages and bonds. Yield rates. [Offered: F,W,S]

# ACTSC 232 – Life Contingencies 1

The future lifetime random variable: Probability and survival functions; force of mortality; complete and curtate expectation of life; Makeham and Gompertz mortality laws. Life tables: Characteristics of population and insurance life tables; selection; fractional age assumptions. Life insurance payments and annuity payments: Present value random variables; expected present values; higher moments; actuarial notation. Annual, 1/mthly and continuous cases. Relationships between insurance and annuity functions. Premiums: Expense loadings. Present value of future loss random variables and distribution, net and gross cases. Equivalence principle. Portfolio percentile principle. Extra risks.

# ACTSC 291 – Corporate Finance 1

This is the first in a two-course sequence that deals with corporate financial decision-making. Topics may include time value of money, capital budgeting, cost of capital, security issuance, capital structure, payout policy and dividends, short term finance, and risk management. Where suitable, topics are treated from a mathematical and quantitative perspective.

# ACTSC 331 – Life Contingencies 2

Policy Values: Annual, 1/mthly and continuous cases. Thiele's equation. Policy alterations. Modified policies. Multiple State Models: Applications in life contingencies; assumptions; Kolmogorov equations; premiums, policy values, multiple decrement models. Joint Life Models: Valuation of insurance benefits on joint lives, dependent and independent cases.

# ACTSC 371 – Introduction to Investments

Introduction to capital markets. Analysis of equity and fixed income investments. Introduction to derivative securities including futures, forwards, swaps and options. [Offered: F,W,S]

# ACTSC 372 – Corporate Finance

Capital budgeting. Real Options. Investment decision using Markowitz and utility theory. Capital Asset Pricing Model. Arbitrage Pricing Theory. Market efficiency. Capital structure and dividend policy. Advanced topics. [Offered: F,W,S]

# ACTSC 391 – Corporate Finance 2

This course is a continuation of AFM 272/ACTSC 291. Topics to be explored are covered under the listing for AFM 272/ACTSC 291.

# ACTSC 431 – Loss Models 1

Models for loss severity: parametric models, effect of policy modifications, tail behaviour. Models for loss frequency: (a, b, 0), (a, b, 1), mixed Poisson models; compound Poisson models, Aggregate claims models: moments and moment generating function: recursion. Classical ruin theory. [Offered: F,S]

# ACTSC 432 – Loss Models 2

Credibility theory: limited fluctuation; Bayesian; Buhlmann; Buhlmann-Straub; empirical Bayes parameter estimation; statistical inference for loss models; maximum likelihood estimation; effect of policy modifications; model selection. [Offered: F,S]

# ACTSC 433 – Analysis of Survival Data

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. [Offered: W]

# ACTSC 445 – Quantitative Enterprise Risk Management

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. [Offered: F,S]

# ACTSC 446 – Mathematics of Financial Markets

This course covers mathematical techniques for no-arbitrage pricing and hedging financial derivatives. Topics to be covered can be classified into three broad areas: 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 Itô's lemma; Black-Scholes model; interest rate models and bond pricing). [Offered: F,W]

# ACTSC 453 – Basic Pension Mathematics

Theory and practice of pension plan funding. Assumptions, basic actuarial functions and population theory applied to private pensions. Concepts of normal costs, supplemental liability, unfunded liability arising from individual accrued benefit and projected benefit cost methods.

# ACTSC 455 – Advanced Life Insurance Practice

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.

# ACTSC 462 – Introduction to Property and Casualty Pricing

An introduction to property/casualty rate making. The economics of insurance. The ratemaking process. Individual risk rating. Reinsurance, expense issues. Pricing for deductibles and increased limits.

# ACTSC 463 – Introduction to Property and Casualty Loss Reserving

An introduction to property/casualty loss reserving techniques. Claim payment process. Chain-ladder methods. Stochastic models.

# ACTSC 468 – Readings in Actuarial Science 1

Reading course as announced by the department.

# ACTSC 469 – Readings in Actuarial Science 2

Reading course as announced by the department.

# ACTSC 471 – Advanced Corporate Finance

This course covers various advanced topics in corporate finance, with emphasis on theories of corporate incentives and asymmetric information. Illustrative applications using cases are provided.

# ACTSC 611 – Financial Mathematics I

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; binomial option valuation. Duration and Immunization

# ACTSC 612 – Life Insurance Mathematics I

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.

# ACTSC 613 – Statistics for Actuarial Science

Discrete and continuous random variables; generating functions; dependence; maximum likelihood estimation, functions of random variables; confidence intervals, hypothesis tests; condition expectation; compound distributions.

# ACTSC 614 – Corporate Finance

Agency theory; investment decisions; long-term financing and cost of capital; principles of taxation; financial reporting; assessment of capital investment projects.

# ACTSC 615 – Economics

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.

# ACTSC 621 – Financial Mathematics II

Mean-Variance portfolio theory; Capital-Asset Pricing Method, Arbitrage Pricing Theory, Efficient Markets Hypotheses; Capital structure and dividend policy.

# ACTSC 622 – Life Insurance Mathematics II

Multiple state models; premiums and reserves for stat dependent policies, including joint life and last survivor benefits; cashflow projection methods; deterministic, stochastic and stress testing; embedded options; introduction to pension valuation and funding.

# ACTSC 623 – Applied Statistics

Generalized linear models: multiple linear regression and normal linear model; exponential family; link functions; linear predicators; estimation; testing. Time series: Univariate ARIMA; multivariate AR; applications to economic series.

# ACTSC 624 – Stochastic Processes for Actuarial Science

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

# ACTSC 625 – Casualty and Health Insurance Mathematics

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.

# ACTSC 631 – Financial Mathematics III

Risk measures, Binomial and lattice models for option pricing, Black-Scholes option pricing; term structure models. Credit risk; types of models and types of derivatives.

# ACTSC 632 – Life Insurance Mathematics III

Estimation for lifetime models; estimation for multiple state modes. Graduation. Mortality projection using the Lee Carter model. MLE for Markov multiple state models.

# ACTSC 633 – Actuarial Risk Management

The Actuarial Profession. The Actuarial Control Cycle Impact of Regulation. Consumer needs. Assessing risk. Modeling. Monitoring Experience. Pricing and reserving in life and non-life insurance.

# ACTSC 634 – Quantitative Risk Management

Enterprise Risk management. Pricing and valuation. Economic and regulatory capital. Solvency. Investment management.

# ACTSC 635 – Profession Communications in Actuarial Science

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

# ACTSC 690 – Literature & Research Studies

# ACTSC 831 – Loss Models 1

Models for loss severity: parametric models, effect of policy modifications; tail behabiour. Models for loss frequency: (a,b,0), (a,b,1), mixed Poisson models; compound Poisson models. Aggregate claims models: moments and moment generating function: recursion. Classical ruin theory.

# ACTSC 832 – Loss Models 2

Credibility theory: limited fluctuation; Bayesian; Buhlmann; Buhlmann-Straub; empirical Bayes parameter estimation statistical inference for loss models; maximum likelihood estimation; effect of policy modifications; model selection.

# ACTSC 833 – Analysis of Mortality Data

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.

# ACTSC 845 – Quantitative Enterprise Risk Management

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.

# ACTSC 846 – Mathematics of Financial Markets

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).

# ACTSC 853 – Basic Pension Mathematics

Theory and practice of pension plan funding. Assumptions, basic actuarial functions and population theory applied to private pensions. Concepts of normal costs, supplemental liability, unfunded liability arising from individual accrued benefit and projected benefit cost methods.

# ACTSC 855 – Advanced Life Insurance Practice

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.

# ACTSC 862 – Introduction to Property and Casualty Pricing

An introduction ot property/casualty rate making. The economics of insurance. The ratemaking process. Individual risk rating. Reinsuance, expense issues. Pricing for dedutibles and increased limits.

# ACTSC 863 – Introduction fo Property and Casuality Loss Reserving

An introduction to property/casualty loss reserving techniques. Claim payment process. Chain-ladder methods, Stochastic models.

# ACTSC 936 – Longitudinal Data Analysis

This course is designed to teach students the appropriate techniques for analyzing data that is collected over time. This data could arise from biomedical, population public health studies as well as finance and actuarial science applications. The course will teach how to recognize the added complexity of longitudinal data versus the univariate response data which is typically seen in introductory and generalized linear model courses. The course emphasizes the importance of the covariance structure for longitudinal responses. The students will study the difference between subject-specific and population-averaged models and how to recognize problems where one or the other approach might be more appropriate. They will be expected to use statistical software in applications in order to analyze longitudinal data.

# ACTSC 961 – Mathematical Methods of Loss Reserving

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.

# ACTSC 963 – Insurance Surplus Mathematics

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.

# ACTSC 964 – Topics in Quantitative Risk Management

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.

# ACTSC 965 – Extreme Value Theory

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.

# ACTSC 966 – Aggregate Claims Models

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.

# ACTSC 970 – Finance 1

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.

# ACTSC 971 – Finance 2

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.

# ACTSC 972 – Finance 3

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.

# ACTSC 973 – Portfolio Optimization

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.

# ACTSC 974 – Financial Econometrics

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.

# ACTSC 980 – Social Insurance

Review of the history and present status of the major Canadian Social Insurance systems such as CPP, Medicare, UIC and OAS. Possible future developments. Costing problems and trends. Financing, past, present and future.