Actuarial Mathematics Courses
ACMA 210 - Mathematics of Compound Interest (3)
Measurement of interest, present value. Equations of value. Basic annuities: immediate, due, perpetuity. General annuities. Yield rates: cash flow analysis, reinvestment rate, portfolio and investment year methods. Amortization schedules and sinking funds. Bonds and other securities. Applications: real estate mortgages depreciation methods. Interest rate disclosure and regulation in Canada. Covers the interest theory portion of Exam FM of the Society of Actuaries. Prerequisite: MATH 152. Students with credit for ACMA 310 may not take this course for further credit. Quantitative.
ACMA 315 - Credibility Theory (3)
Limited fluctuation credibility theory: full credibility, partial credibility. Greatest accuracy credibility theory: the Bayesian methodology, the credibility premium, the Buhlmann model, the Buhlmann-Straub model, exact credibility, linear versus Bayesian versus no credibility. Empirical Bayes parameter estimation: nonparametric estimation, semiparametric estimation, parametric estimation. Simulation: basics of simulation, simulation in actuarial modeling. Covers part of the syllabus for Exam C of the Society of Actuaries, and Exam 4 of the Casualty Actuarial Society. Prerequisite: STAT 285. Quantitative.
ACMA 320 - Actuarial Mathematics I (5)
Survival distributions: age at death, life tables, fractional ages, mortality laws, select and ultimate life tables. Life insurance: actuarial present value function (apv), moments of apv, basic life insurance contracts, portfolio. Life annuities: actuarial accumulation function, moments of apv, basic life annuities. Net annual premiums: actuarial equivalence principle, loss function, accumulation type benefits. Actuarial reserves: prospective loss function, basic contracts, recursive equations, fractional durations. Covers part of the syllabus for Exam M of the Society of Actuaries and Exam 3 of the Casualty Actuarial Society, and covers practical applications such as computational aspects of pricing and reserving, and risk measurement of insurance portfolios. Prerequisite: STAT 285 and ACMA 210 (with a grade of C+ or higher). Quantitative.
ACMA 335 - Risk Theory (3)
Basic distributional quantities: moments, percentiles, generating functions and sums of random variables. Classifying and creating distributions. Frequency and severity with coverage modifications: deductibles, the loss elimination ratio and the effect of inflation for ordinary deductibles, policy limits, coinsurance. Aggregate loss models. Multi-state transition models with actuarial applications: non-homogeneous Markov chains, cash flows and their actuarial present values. The exponential distribution and the Poisson process. Covers part of the syllabus for Exam M of the Society of Actuaries, and Exam 3 of Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.
ACMA 395 - Special Topics in Actuarial Science (3)
Topics in areas of actuarial science not covered in the regular certificate curriculum of the department. Prerequisite: Dependent on the topics covered.
ACMA 425 - Actuarial Mathematics II (3)
Actuarial reserves: allocation of the loss to the policy years. Multiple life functions: joint-life, last-survivor. Multiple decrement models: stochastic and deterministic approaches, associated single decrement, fractional durations. Valuation theory for pension plans. Insurance models including expenses: gross premiums and reserves, type of expenses, modified reserves. Nonforfeiture benefits and dividends: equity concept, cash values insurance options, asset shares, dividends. Covers part of the syllabus for Exam M of the Society of Actuaries and Exam 3 of the Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.
ACMA 445 - Loss Models: Estimation and Selection (3)
Quality of an estimator: unbiasedness, asymptotic unbiasedness, consistency, means squared error, uniform minimum variance. Confidence interval. Tests of hypotheses. Estimation for complete data. Estimation for grouped data. Estimation for modified data: Kaplan-Meier estimator, variances and confidence intervals of the empirical estimator, kernel density estimator. Parameter estimation. Variance of the estimators and confidence intervals. Model selection: graphical procedures, goodness-of-fit test, likelihood ratio test. Interpolation and smoothing. Covers part of the syllabus for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.
ACMA 465 - Mathematics of Demography (3)
Data: Sources and Errors. Measures of mortality and fertility: Crude rates, Age-specific mortality rates, Adjusted measures of mortality. Construction of Life Tables from census data: 1989-91 U.S. Life Table, 1990-92 Canadian Life Table. Stationary Population Theory: survivorship group, Lexis diagram. Stable Population Theory: Sharpe-Lotka theorem, growth rate, quasi-stable populations. Population Projections: logistic curve, component method. Uses of Census Data: Funding Social Security. Prerequisite: ACMA 320. Students with credit for STAT 490 or ACMA 490 may not take this course for further credit. Quantitative.
ACMA 470 - Property and Casualty Insurance (3)
Ratemaking: terminology, process, trend, ultimate losses, expense provisions, profit and contingencies, overall rate indications, classification rates, increased limits. Individual risk rating: prospective systems, retrospective rating, design. Loss Reserving: accounting concepts, definitions, principles, loss reserving process. Risk classification: relationship to other mechanisms, criteria for selecting rating variables, examples, efficiency, estimating class relativities. Covers part of the syllabus for Exam 5 of Casualty Actuarial Society. Prerequisite: ACMA 320. Students with credit for ACMA 490 or STAT 490 may not take this course for further credit. Quantitative.
ACMA 475 - Theory of Pension (3)
Overview of pension plans: design, funding, regulation, accounting standards. Pension funding methods: actuarial cost methods, terminal funding method. Individual actuarial cost methods: accrual benefit cost method, entry-age actuarial cost method, unit-credit method, individual-level-premium method, attainted-age-normal method. Group actuarial cost methods. Prerequisite: ACMA 320. Corequisite: ACMA 425. Students with credit for STAT 490 or ACMA 490 may not take this course for further credit. Quantitative.
ACMA 490 - Selected Topics in Actuarial Science (3)
The topics included in this course will vary from term to term depending on faculty availability and student interest. Prerequisite: Dependent on the topic covered.
ACMA 495 - Directed Studies in Actuarial Science (3)
Independent study and/or research in topics chosen in consultation with the supervising instructor. Prerequisite: written permission from the Department of Statistics and Actuarial Science undergraduate curriculum committee.
ACMA 815 - Rate of Return Models (2)
An introduction to stochastic models for the rate of return. Time series. Stochastic differential equations. Covariance equivalence principle. Applications. Prerequisite: Permission of the Department. Students with credit for ACMA 820 may not take this course for further credit.
ACMA 816 - Stochastic Claims Processes (2)
Study the distribution of aggregate claims and introduce stochastic claims reserving methods in insurance. Individual versus collective models. Standard distribution-free methods. Other models. Prerequisite: Permission of the Department. Students with credit for ACMA 821 may not take this course for further credit.
ACMA 820 - Stochastic Analysis of Insurance Portfolios (4)
Life insurance models. Interest rate models for life insurance: time series, stochastic differential equations, estimation. Portfolios of identical policies. Diversified portfolios. Prerequisite: ACMA 320.
ACMA 821 - Advanced Actuarial Models (4)
Advanced non-life insurance mathematics. Individual risk models, collective risk models, ruin models. Actuarial reserve models: Bonus-malus system, IBNR techniques. Generalized linear models in Actuarial Science. Prerequisite: ACMA 335.
ACMA 822 - Risk Measures and Ordering (4)
Actuarial risks. Insurance premium calculation principles and properties. Risk measures and ordering. Applications. Prerequisite: ACMA 335.
ACMA 850 - Actuarial Science: Selected Topics (4)