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# Undergraduate Program in Statistics and Actuarial Science

The statistics and actuarial science programs train students for a variety of careers.  Statisticians deal with organization, analysis, and presentation of data.  Actuaries establish the procedures used by the insurance industry.

Statisticians in business are involved in management information systems, analysis of consumer behavior, investment analysis, inventory control, and many other tasks.  The pharmaceutical industry is one of the largest employers of statisticians, and here the statisticians are instrumental in design and and evaluating drug testing protocols. Actuaries apply mathematics, probability, and statistics to the fields of insurance and pension management.  Most actuaries are employed by the insurance industry, but many are now finding careers in pension management, health care industries, government, and private consulting.

A.  Programs of Study
B.  Statistics Courses
C.  Actuarial Science Program Handbook

A.  Programs of Study
1.  Career Preparation

The programs offer students the theory and techniques for the use of mathematics in solving business problems. Each course places special emphasis on methods that solve actual problems. Students work extensively with computers and statistical software.

Statistics is a recommended comajor of all the functional areas of the Stern School, particularly because of the Internet and the ubiquity of large databases.

Qualification as an actuary requires passing a series of professional examinations given by either the Society of Actuaries (for life insurance and pensions) or by the Casualty Actuarial Society (property and casualty insurance).  The department's courses prepare students for the content of the first two of these exams, along with substantial preparation for material beyond the second exam.  The objective is the attainment of an associateship designation within these professional societies.  The societies have reorganized the professional examinations, effective 2000, to include substantial components of finance and economics.  Stern is one of only a few schools that has a program ideally matched to the needs of the actuarial profession.

2. Statistics Major Requirements (12 points)

To qualify as an undergraduate statistics major, a student must take

Either:

STAT-UB.0015 (C22.0015) Statistical Inference & Regression Analysis
or
STAT-UB.0017 (C22.0017) Regression & Multivariate Data Analysis

and any three of the following courses:

STAT-UB.0055 (C20.0055) Financial Engineering*
STAT-UB.0008 (C22.0008) Applied Stochastic Processes for Financial Models*
STAT-UB.0014 (C22.0014) Introduction to the Theory of Probability**
STAT-UB.0015 (C22.0015) Statistical Inference & Regression Analysis (if not already selected)**
STAT-UB.0017 (C22.0017) Regression & Multivariate Data Analysis (if not already selected)*
STAT-UB.0018 (C22.0018) Forecasting of Time Series Data*
STAT-UB.0021 (C22.0021) Introduction to Stochastic Processes**
STAT-UB.0027 (C22.0027) Mathematics of Investment**
STAT-UB.0027 (C22.0037) Life Contigencies**
STAT-UB.0057 (C22.0057) Data Mining and Business Intelligence*
MULT-UB.0007 (C70.0007) Decision Models*

* Courses that require only the business core at the Stern School of Business.
** Courses that have additional mathematics and other prerequisite requirements.

It is highly recommended that a student do a double major if statistics is selected as one of the majors.

As soon as they begin, students in the statistics major should consult with their adviser in the Office of Undergraduate Advising and Student Services concerning intensive statistics as a major to ensure that course distribution requirements are being met.  In their sophomore year, students should meet with their adviser to declare formally the intensive statistics major.  The statistics and actuarial science undergraduate program coordinator is always available to advise on statistics course selection or other matters intensive statistics students may wish to discuss.

3.  Actuarial Science Major Requirments (31 points)

Each course carriers 3 points, except as noted.

V63.0121 Calculus I (in lieu of V63.0017), 4 points
V63.0122 Calculus II, 4 points
V63.0123 Calculus III, 4 points
V63.0124 Linear Algebra, 4 points
FINC-UB.0007 (C15.0007) Financial Management
STAT-UB.0014 (C22.0014) Introduction to the Theory of Probability
STAT-UB.27 (C22.0027) Mathematics of Investment
Plus two of the following four courses:
1. STAT-UB.0015 (C22.0015) Statistical Inference and Regression Analysis
2. STAT-UB.0018 (C22.0018) Forecasting of Time Series Data
3. STAT-UB.0021 (C22.0021) Introduction to Stochastic Processes
4. STAT-UB.0037 (C22.0037) Life Contingencies

Students majoring in actuarial science should consult with their adviser in the Office of Undergraduate Advising and Student Services by the end of their sophomore year to ensure that course distribution requirements are being met and to declare formally the actuarial science major.  The statistics and actuarial science undergraduate program coordinator is always available to advise on actuarial science course selection or other matters actuarial science students may wish to discuss.

4.  Marketing Research Specialization Requirements (24 points)

Students interested in a market research specialization should choose to double major in statistics and marketing.  One of their marketing course selections should be FINC-UB.0009 (C15.0009) Marketing Research.

Students choosing the specialization should consult with their adviser in the Office of Undergraduate Advising and Student Services by the end of their sophomore year to ensure that course distribution requirements. Students are advised to consult the Undergraduate Coordinators in Statistics (Aaron Tenenbein) and Marketing (Sunder Narayanan) for selecting a course of study.

B.  Statistics Courses

• STAT-UB.0103 (C22.0103) Statistics for Business Control and Regression and Forecasting Models  (6 pts)
• STAT-UB.0001 (C22.0001) Statistics for Business Control (4 pts)
• STAT-UB.0003 (C22.0003) Regression and Forecasting Models (2 pts)

• STAT-UB.0008 (C22.0008) Applied Stochastic Processes for Financial Models
• STAT-UB.0010 (C22.0010) Categorical Data
• STAT-UB.0011 (C22.0011) Sampling Techniques
• STAT-UB.0014 (C22.0014) Introduction to the Theory of Probability
• STAT-UB.0015 (C22.0015) Statistical Inference and Regression Analysis
• STAT-UB.0017 (C22.0017) Regression and Multivariate Data Analysis
• STAT-UB.0018 (C22.0018) Forecasting Time Series Data
• STAT-UB.0021 (C22.0021) Introduction to Stochastic Processes
• STAT-UB.0027 (C22.0027) Mathematics of Investments
• STAT-UB.0037 (C22.0037) Life Contingencies
• Independent Study

Statistics for Business Control and Regression and Forecasting Models
STAT-UB0103 (C22.0103).  6 points.  Fall, spring, summer.
Prerequisites: INFO-UB.0001 (C20.0001), V63.0017 or V63.0121, and sophomore standing.  This course combines STAT-UB.0001(C22.0001) and STAT-UB.0003 (C22.0003).

Modern statistical methods as a basis for decision making in the face of uncertainty.  Topics include probability theory, discrete and continuous distributions, hypothesis testing, estimation, and statistical quality control.  With the aid of the computer, these statistical methods are used to analyze data.  Also presented is an introduction to statistical models and their application to decision making.  Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, multiple regression analysis, introduction to time series analysis, and exponential smoothing.

STAT-UB.0001 (C22.0001).  4 points.  Fall and spring.
This course is not to be taken by students who have taken STAT-UB.0103 (C22.0103).
Prerequisites:  INFO-UB.0001 (C20.0001), V63.0017 or V63.0121, and sophomore standing.

Modern statistical methods as a basis for decision making in the face of uncertainty.  Topics include probability theory, discrete and continuous distributions, hypothesis testing, estimation, and statistical quality control.  With the aid of the computer, these statistical methods are used to analyze data.  Also presented is an introduction to statistical models and their application to decision making.  Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, multiple regression analysis, introduction to time series analysis, and exponential smoothing.

Regression and Forecasting Models
STAT-UB.0003 (C22.0003).  2 points.  Fall, spring, summer.
This course is not to be taken by students who have taken STAT-UB.0103 (C22.0103).
Prerequisite:  STAT-UB.0001 (C22.0001) or equivalent.

An introduction to statistical models and their application to decision making.  Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, multiple regression analysis, introduction to time series analysis, and exponential smoothing.

Applied Stochastic Processes for Financial Models
STAT-UB.0008 (C22.0008).  3 points.  Fall and spring.
Cross-listed with STAT-GB.2308 (B90.2308).  Prerequisite: C22.09103 or C22.0003.

Presents a mathematical background for the stochastic processes that are widely employed as modeling tools in finance.  The emphasis is on an intuitive approach and examples rather than on proofs and mathematical rigor.  Topics include random walks, martingales, Markov chains, Poisson process and other continuous time Markov chains, Brownian motion, geometric Brownian motion, and other diffusion processes.  The relevance of the considered processes to financial modeling is stressed throughout.  In particular, applications to pricing of derivative securities and to modeling of the term structure to interest rates are discussed.

Categorical Data
STAT-UB.0010 (C22.0010).  3 points.  Fall.
Cross-listed with STAT-GB.3307 (B90.3307).  Prerequisite: STAT-UB.0015 (C22.0015).

Introduces discrete random variables, with most of the emphasis going to the bivariate and multivariate situations.  Major topics are the chi-squared statistic, Fisher's exact test, odds ratio estimates and intervals, sets of tables, the log-linear model, model fitting, and logit analysis.  Minor topics that may be covered are the Mantel-Haenszel statistic, rate standardizing, and detailed modeling of interaction in the two-dimension table.

Sampling Techniques

STAT-UB.0011 (C22.0011).  3 points.  Spring.
Cross-listed with STAT-GB.3308 (B90.3308).  Prerequisite: STAT-UB.0015 (C22.0015)

Considers commonly used sampling schemes such as simple, random, stratified, multistage, and double sampling and examines their efficiency.  Studies methods of estimation, including ratio and regression.  Other topics include poststratification, multivariate surveys, analytic studies, problems of nonresponse, nonsampling errors, and randomized response technique.  Theory is illustrated with examples from diverse fields.

Introduction to the Theory of Probability
STAT-UB.0014 (C22.0014).  3 points.  Fall and spring.
Cross-listed with STAT-GB.3301 (B90.3301).  Prerequisites: V63.0121 and V63.0122.

Covers the basic concepts of probability.  Topics include the axiomatic definition of probability; combinatorial theorems; conditional probability and independent events; random variables and probability distributions; expectation of functions of random variables; special discrete and continuous distributions, including the chi-square, t, F, and bivariate normal distributions; law of large numbers; central limit theorem; and moment generating functions.  The theory of statistical estimation is introduced with a discussion on maximum likelihood estimation.

Statistical Inference and Regression Analysis

STAT-UB.0015 (C22.0015).  3 points.  Fall and spring.
Cross-listed with STAT-GB.3302 (B90.3302).  Prerequisites: V63.0121, V63.0122, and STAT-UB.0014 (C22.0014).

Consists of two distinct components:  statistical inference and regression analysis.  Statistical inference topics include the principles of statistical estimation and inference, Neyman Pearson Lemma, testing of means, variances, tests of independence, and nonparametric methods.  Regression analysis discusses the general linear regression model, least squares estimation, departures from standard assumptions, autocorrelation, multicollinearity, analysis of residuals, choice of variables, and nonlinear models.

Regression and Multivariate Data Analysis

STAT-UB.0017 (C22.0017).  3 points.  Fall and spring.
Cross-listed with STAT-GB.2301 (B90.2301) and STAT-GB.3312 (B90.3312).  Prerequisite: STAT-UB.0103 (C22.0103) or STAT-UB.0003 (C22.0003).

This is a data-driven, applied statistics course focusing on the analysis of data using regression models. It emphasizes applications to the analysis of business and other data and makes extensive use of computer statistical packages. Topics include simple and multiple linear regression, residual analysis and other regression diagnostics, multicollinearity and model selection, autoregression, heteroscedasticity, regression models using categorical predictors, and logistic regression. All topics are illustrated on real data sets obtained from financial markets, market research studies, and other scientific inquiries.

Forecasting Time Series Data

STAT-UB.0018 (C22.0018).  3 points.  Fall and spring.
Cross-listed with STAT-GB.2302 (B90.2302) and STAT-GB.3312 (B90.3312).  Prerequisite: STAT-UB.0103 (C22.0103) or STAT-UB.0003 (C22.0003).

An exposition of time series and forecasting techniques with emphasis on ideas, methods, and interpretations.  Discusses the determination of the best analytical model for a given problem and the application of this model in the decision-making process for purposes that include description, explanation, and control of time-dependent data.  Illustrates all techniques with case studies and uses computer program packages as an aid for obtaining solutions.  The major focus is the Box-Jenkins approach to modeling and forecasting time series.  Topics include model building, model selecting, descriptions of timing and correlation relationships among data sets and forecasting models, estimation, and diagnostic checking.  Other topics are seasonal adjustment, exponential smoothing models, state space models, and nonlinear models.

Introduction to Stochastic Processes

STAT-UB.0021 (C22.0021).  3 points.  Fall.
Cross-listed with STAT-GB.3321 (B90.3321).

An introductory course in stochastic processes.  Presents classes of stochastic processes, which are widely used as modeling tools in many fields of application, including finance, economics, accounting,and actuarial science.  Covers basic theory of discrete and continuous time Markov chains, Brownian motion and its generalizations, and martingales.  Also discusses statistical aspects o these processes.  In the final part of the course, introduces the idea of stochastic integration and develops the rules of stochastic calculus.  If time permits, also considers some stochastic differential equations.

Mathematics of Investments

STAT-UB.0027 (C22.0027).  3 points.  Fall.
Cross-listed with STAT-GB.2309 (B90.2309).  Prerequisites: V63.0121, V63.0122.

Discusses the mathematical and technical aspects of investments.  Topics include measurement of interests and discount rates, accumulated value and present value, annuities, sinking funds, amortization of debt, and determination of yield rates on securities.  Applications include bond evaluation, mortgages, capital budgeting, and depreciation methods.

Life Contingencies

STAT-UB.0037 (C22.0037).  3 points.  Spring.
Cross-listed with STAT-GB.3335 (B90.3335).  Prerequisites: STAT-UB.0014 (C22.0014) and STAT-UB.0027 (C22.0027).

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, joint life probabilities and annuities, and multiple decrement theory. Applications to pension plans are discussed.

Independent Study in Statistics, Operations Research, or Actuarial Science

Prerequisite: permission of the undergraduate program coordinator.

For selected students whose academic records indicate ability to conduct independent research.  Each student makes an intensive study of some topic of his or her own choosing, subject to the approval of the instructor.  Included are seminar sessions. for group discussions of the various projects.

## Questions about Statistics or Actuarial Science Program?

Contact:  Aaron Tenenbein
Statistics and Actuarial Science Program Advisor
Room 8-50 KMC, 212-998-0474
atenenbe@stern.nyu.edu