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Actuarial Classes offered at Stern
C22.0014/B90.3301: Introduction to the Theory of Probability
Covers the basic concepts of probability. Topics include the axiomatic
definition of probability; combinatorial theorems; conditional probability
and independent events; random variables and probability distribution;
expectation of functions of random variables; special discrete and
continuous distributions, including the chi-square, t, and F-distributions,
with emphasis on the bivariate normal distribution; law of large numbers;
central limit theorem; and moment generation functions.
C22.0015/B90.3302: Statistical Inference and Regression Analysis
The course has two distinct components: statistical inference and regression
analysis. Topics included in statistical inference are: Principles of
statistical estimation and inference; Neyman Pearson Lemma, testing of
means, variances, tests of independence, Non-parametric methods. Regression
analysis will discuss the general linear regression model; least squares
estimation, departures from standard assumptions, autocorrelation,
multicollinearity; analysis of residuals; choice of variables; non-linear
models.
C22.0018/B90.2302: Forecasting Time Series Data
In this course, we cover practical time series forecasting techniques with
emphasis on the Box-Jenkins (ARIMA) method and conditional volatility
(ARCH/GARCH) models. We provide a mix of practical data analysis as well as
an introduction to the relevant theory. The Arima models are used to
forecast series like interest spreads while ARCH models are used in
estimating returns. Students analyze data sets of their own choice in
projects. Additional topics of interest covered in the course are methods of
testing for nonstationary (Dickey-Fuller tests_ as well as models for
capturing seasonality as seen for example in series of monthly sales
figures. The low-cost forecasting method of exponential smoothing is
discussed and its connection the the RiskMetrics methods of J.P. Morgan and
GARCH models is explored. If time permits, we also study methods of
forecasting multivariate time series, where information from several series
is pooled to forecast a single series. The concept of co-integration or
co-movement of multivariate series is discussed (interest rates being a
prime example) along with their implications for forecasts. Other potential
topics in the course include the use of ARCH models in value at risk (VAR)
analysis as in option pricing.
C22.0027/B90.2309: Mathematics of Investment
The course discusses the mathematical and technical aspects of investments.
Topics include: Measurement of interest and discount rates, accumulated
value and present value, annuities, sinking funds, amortization of debt,
determination of yield rates on securities. Applications include: bond
evaluation, mortgages, capital budgeting, depreciation methods, and
insurance.
C22.0037: Life Contingencies
Applies probability and mathematics of investment to problems of premiums
and reserves on annuities and insurance policies. Topics include
probabilities of mortality, laws of mortality, join life probabilities and
annuities, multiple decrement theory. Applications to pension plans is
discussed.
B90.3321/C22.0021: Stochastic Processes I
This is an introductory course in stochastic processes. The topics included
discrete and continuous time Markov chains, martingales, and Brownian
motion. Statistical aspects and applications of these processes to various
fields are also discussed. |
