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Actuarial Science
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The field of actuarial science applies mathematical principles and techniques to problems in the insurance industry. Progress in the field is generally based upon completion of examinations given by the Society of Actuaries (SOA). The Baruch College major is designed to prepare students to pass the first five examinations. Students interested in this highly structured program are urged to contact the Department of Mathematics as early as possible so that the department may assign an advisor to aid in formulating an appropriate course of study.
Program Learning Goals
Upon completion of the required core courses in actuarial mathematics, students will be able to:
Examine and solve problems dealing with discrete and continuous probability distributions.
Recognize when a specific probability distribution is applicable.
Determine an appropriate distribution to model a specific scenario in a risk-management context.
Compute equivalent interest and discount rates (both nominal and effective).
Write an equation of value for a set of cash flows. Estimate effective compound yield rates for the set of cash flows using a simple interest approximation.
Calculate present and future values for various types of annuities and perpetuities such as annuities-due, perpetuities-due, annuities-immediate, perpetuities-immediate, arithmetic or geometric annuities, and non-level annuities.
Determine the payment amount for a loan with a specific repayment structure.
Find the outstanding balance immediately after a payment on a loan.
Calculate the amount of principal and amount of interest in a payment for an amortized loan.
Perform an amortization on a coupon bond.
Compute yield rates for a callable bond at each of the call dates.
Calculate values, duration, and convexity for both zero-coupon bonds and coupon bonds.
Use first-order approximation methods based on duration to estimate the change in present value of a portfolio based on changes in interest rates.
Construct an investment portfolio to immunize a set of liability cash flows.
Calculate minimal variance portfolios with and without constraints.
Perform pricing and hedging of European and American type derivative securities in the context of one- and multi-period binomial models.
Construct arguments based on the no-arbitrage principle, and devise arbitrage strategies when this principle is violated.
Price European derivative securities in the context of the Black-Scholes model.
Derive a put-call parity relation, and use it for pricing and hedging.
Upon completion of elective courses in actuarial mathematics, students will be able to:
Find closed-form solutions to ordinary and partial differential equations derived from financial models.
Derive the celebrated Black-Scholes formula by solving the Black-Scholes PDE.
Compute values of European, American, and exotic options using finite difference numerical methods.
Download options market data and use it as input for codes generating implied volatility surfaces.
Describe and classify different kinds of short-term insurance coverage.
Explain the role of rating factors and exposure in pricing short-term insurance.
Create new families of distributions by applying the technique of multiplication by a constant, raising to a power, exponentiation, or mixing.
Calculate various measures of tail weight and interpret the results to compare tail weights.
Calculate risk measures, including Value at Risk and Tail Value at Risk, and explain their properties, uses, and limitations.
Calculate premiums using the pure premium and loss ratio methods.
Use Maximum Likelihood Estimation and Bayesian Estimation to estimate parameters for severity, frequency, and aggregate distributions for individual, grouped, truncated, or censored data.
Use hypothesis tests (e.g., Chi-square goodness-of-fit, Kolmogorov-Smirnov, and likelihood ratio tests) and score-based approaches (e.g., the Schwarz-Bayesian Criterion, the Bayesian Information Criterion, and the Akaike Information Criterion) to perform model selection on a collection of data.
Apply credibility models such as the Buhlmann and Buhlmann-Straub models, and explicate the relationship between these models and Bayesian models.
Explain the concepts of random sampling, statistical inference and sampling distribution.
State and use basic sampling distributions.
Describe and apply the main methods of estimation including matching moments, percentile matching, and maximum likelihood.
Describe and apply the main properties of estimators including bias, variance, mean squared error, consistency, efficiency, and UMVUE.
Construct confidence intervals for unknown parameters, including the mean, differences of two means, variances, and proportions.
Analyze data using basic statistical inference tools like confidence intervals and hypothesis testing for the population mean.
Apply tools such as analysis of variance, tests of significance, residual analysis, model selection, and predication in both the simple and multiple regression models.
Demonstrate proficiency in some basic programming skills in SAS and the time-series Forecasting interactive system. Perform time-series analysis using these tools.
Identify patterns in data such as trend or seasonality. Incorporate these patterns into the time-series analysis of the data, and perform error analysis of the data.
Explain K-means and hierarchical clustering, and interpret the results of a cluster analysis.
Common Objectives – Actuarial and Financial Mathematics
Upon completion of the required finance courses for the actuarial science and financial mathematics majors, students will be able to:
Expound on the governance of corporations.
Outline the operation of financial markets and institutions.
Measure corporate performance.
Analyze risk and return. Determine the opportunity cost of capital.
Perform capital budgeting using various techniques.
Compute the present and future values of investments with multiple cash flows.
Describe the mechanisms that cause fluctuation of bond yields.
Calculate internal rate of return.
Perform and interpret scenario analysis for a proposed investment.
Calculate financial break-even points.
Determine relevant cash flows for a proposed project.
Determine a firm’s overall cost of capital.