Actuarial Science Course Descriptions

01:640:478 Probability II (3)
Sums of independent random variables, moments and moment-generating functions, characteristic functions, uniqueness and continuity theorems, law of large numbers, conditional expectations, Markov chains, random walks. Prerequisites: 01:640:250 and either 01:640:477 or both 01:640:251 and 01:960:381.

56:645:582 Probability and Actuarial Mathematics (3)Basic probability structures, probability distributions, random number generations and simulations; Moments and its generating functions, Functions of Random variables and Sampling Distributions; Central Limit Theorem, Law of Large numbers, Order Statistics and its distribution. Prerequisite: Calculus

16:960:580 Basic Probability (Cr. 3)
Prerequisite: One year of Calculus. Credit given for only one of 16:960:580, 582, 592.
Discrete probability spaces, combinatorial analysis, occupancy and matching problems, basic distributions, probabilities in a continuum; random variables, expectations, distribution functions, conditional probability and independence; coin tossing, weak law of large numbers, deMoivre-Laplace theorem.

16:960:582 Introduction to Methods and Theory of Probability (Cr. 3)
Prerequisite: One year of Calculus. Credit given for only one of 16:960:580, 582, 592.
Emphasis is on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, sampling distributions.

16:960:563 Regression Analysis (3)
Review of basic statistical theory and matrix algebra; general  regression models; computer application to regression  techniques;  residual analysis; selection of regression models; response surface methodology; experimental design models; and analysis of covariance.  Emphasis on applications. Prerequisite: Level IV statistics.

56:645:567 Statistical Models (3)
Introduction to Multiple Linear Regressions and its diagnostics. Estimation and testing in regression. Analysis of variance models (ANOVA), Regularized Regression: Ridge and Lasso. Generalized Linear Models. Prerequisite: Statistics

16:137:508/56:137:508 Introduction to Financial Mathematics (3)
New course in development

56:645:569 Actuarial Models (3)
Distribution theory and its convolution, application to loss models, failure times and censored data models.  Survival Models: Parametric and Non-Parametric, Estimation and model building.
Prerequisite: 56:645:567 or equivalent.

16:960:542 Life Data Analysis (3)
Statistical methodology for survival and reliability data. Topics include life-table techniques; competing risk analysis; parametric and nonparametric inferences of lifetime distributions; regressions and censored data; Poisson and renewal processes; multistate survival models and goodness-of-fit test. Statistical software used. Prerequisites: One year of calculus and Level V statistics.

16:960:565 Applied Time Series Analysis (3)
Model-based forecasting methods; autoregressive and moving average models; ARIMA, ARMAX, ARCH, and state-space models; estimation, forecasting and model validation; missing data; irregularly spaced time series; parametric and nonparametric bootstrap methods for time series; multiresolution analysis of spatial and time-series signals; and time-varying models and wavelets. Prerequisite: Level V statistics.

16:540:530 Forecasting and Time Series Analysis (3)
Stationary and nonstationary time-series models for purposes of prediction. Estimating trend and seasonality. Various estimation and forecasting techniques. Smoothing techniques.  Prerequisites: Calculus, statistics.

56:645:565 Time Series & Forecasting (3)
Introduction to time series models, Stationary Processes, Measure of Dependence, Tests of Randomness, Forecasting, Estimation, Model selection, ARIMA & ARMA models, Bootstrapping & Smoothing. Prerequisite:56:645:567 or equivalent.

16:711:631 Financial Mathematics II (3)
Options, futures and other derivatives, arbitrage pricing, Black-Scholes theory, exotic options, interest-rate models, stochastic programming models, and their applications to financial planning. Prerequisites: 16:198:521, 01:960:381.

16:711:531 Actuarial Mathematics (3)
Economics of insurance, life tables, life insurance, life annuities, benefit premiums and reserves, multiple-life theory, multiple-decrement models, risk theory, and population theory. Prekopa. Prerequisite: 01:960:381 or 16:640:477.

16:960:554 Applied Stochastic Processes (3)
Markov chains; recurrence; random walk; gambler's ruin; ergodic theorem and stationary distribution; continuous time Markov chains; queuing problems; renewal processes; martingales; Markov processes; Brownian motion; concepts in stochastic calculus; and Ito's formula. Prerequisites: Advanced calculus, and 16:960:580 or 582 or 592.

16:960:654 Stochastic Processes (3)
Selected topics from the theory of the Markov processes, queuing theory, birth and death processes, martingale theory, and Brownian motion and related topics. Measure-theoretic notations, as well as ideas from classical analysis used as needed. Prerequisite: 16:960:554 or 16:960:680.

01:640:477 Mathematical Theory of Probability (3)
Basic probability theory in both discrete and continuous sample spaces, combinations, random variables and their distribution functions, expectations, law of large numbers, central limit theorem. Prerequisite: CALC3. Credit not given for both this course and 01:198:206, 14:332:321, or 01:960:381.

01:960:484 Basic Applied Statistics (3)
Prerequisite: One of the following coures: 960:201, 211, 285, 379, 381, 401 or an equivalent course in basic probability theory. See credit restrictions for Level II Statistics. Estimation, hypothesis testing, chi-square methods, correlation and regression analysis, basis of design of experiments.

16:642:621,622 Financial Mathematics I,II (3,3)  
Introduction to stochastic processes, stochastic calculus and their application to continous-time finance and the mathematical theory of derivative security pricing.
Prerequisites: Probability Theory (Math 01:640:477), Calculus IV (Math 01:640:244), and Linear Algebra (Math 01:640:250).

16:642:624 Credit Derivative Modeling (3)
Single name credit derivatives; structural, reduced form or intensity models; credit default swaps; multiname credit derivatives; top-down and bottom-up models; collateralized debt obligations; tranche options; risk management.

16:960:580 Basic Probability (3)
Discrete-probability spaces; combinatorial analysis; occupancy and matching problems; basic distributions; probabilities in a continuum; random variables; expectations; distribution functions; conditional probability and independence; coin tossing; weak law of large number; and the deMoivre-Laplace theorem. Prerequisite: 16:640:152; effective fall 2009: 16:640:251. Credit given for only one of 16:960:580, 582, 592.

16:960:582 Introduction to Methods and Theory of Probability (3)
Emphasis on methods and problem solving. Topics include probability spaces, basic distributions, random variables, expectations, distribution functions, conditional probability and independence, and sampling distributions. Prerequisite: 16:640:152; effective fall 2009: 16:640:251.  Credit given for only one of 16:960:580, 582, 592.