# 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.