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Course Descriptions
Prereq: MATH 208/208H and STAT 462, or parallel, and both with a grade of “Pass” or "C" or better.
Applications of calculus-based probability, both univariate and multivariate, to risk management-related problems. Problems of the type posed on Society of Actuaries Exam P/Casualty Actuarial Society Exam 1 are covered: determination of loss frequency distributions and their characteristics such as expected value, variance, percentiles; determination of loss severity distributions and their characteristics such as expected value, variance, percentiles; and determination of loss sharing parameters such as deductibles and maximum payments.
Prereq: ACTS 440/840 or parallel.
Application of the basic mathematics of finance to problems involving valuation of financial transactions. Problems of the type posed on Society of Actuaries Exam FM/Casualty Actuarial Society Exam 2 are covered. Determining equivalent measures of interest; estimating the rate of return on a fund; discounting or accumulating a sequence of payments with interest; determining yield rate, length of investment, amounts of investment contributions or amounts of investment returns for various types of financial transactions; and basic calculations involving yield curves, spot rates, forward rates, duration, convexity, immunization and short sales; intruduction to financial derivatives, (forwards, options, futures, swaps) and their use in risk management; and introduction to the concept of no-arbitrage as a fundamental concept in financial mathematics.
Prereq: ACTS 470/870, 471/871, and 473/873.
Problems of the type posed on Society of Actuaries Exam M or Casualty Actuarial Society Exam 3 are covered. Such problems involve: survival and severity models; frequency models; compound (aggregate) models; life contingencies; simple models with stochastic interest rates; and no-arbitrage pricing; Markov Chain models; life contingencies; and Poisson processes.
Prereq: ACTS 410 and 425.
Problems of the type posed on Society of Actuaries Exam C/Casualty Actuarial Society Exam 4 are covered. Such problems involve: construction of empirical models; construction and selection of parametric models; credibility theory; interpolation and smoothing of data; and simulation.
Prereq: ACTS 440, FINA 467 or permission.
Problems as posed in the Society of Actuaries (SOA) Exam “M”. Interest rate models; rational valuation of derivative securities (option procing: put-call parity, the binomial model, Black-Scholes formula, and actuarial applications; interpretation of option Greeks and delta-hedging; features of exotic options; an introduction to Brownian motion and Itô’s lemma); and risk management techniques.
Prereq: STAT 463 or permission.
Full, partial, Buhlmann, and Buhlmann-Straub credibility models; an introduction to empirical Bayes and statistical distributions used to model loss experience; application of polynomial splines to actuarial data; simulation of both discrete and continuous random variables in context of actuarial models; simulation to estimate p-value of hypothesis test; bootstrap method to estimate the mean squared error of an estimator.
Prereq: STAT 463 with a grade of C or better.
Parametric and tabular survival models. Estimation based on observations which may not be complete. Concomitant variables. Use of population data. Applications to groups of impaired lives.
Prereq: STAT 463 with a grade of "C" or better.
Introduction to forecasting in actuarial science. Simple and multiple regression, instrumental variables, time series methods and applications of these methods in forecasting actuarial variables such as interest rates, inflation rates, and claim frequencies. Data sets processed and analyzed using statistical software.
Prereq: MATH 208 with grade of “Pass” or "C" or better.
Application of financial mathematics to problems involving valuation of financial transactions, including: equivalent measures of interest; rate of return on a fund; discounting or accumulating a sequence of payments with interest; and yield rates, length of investment, amounts of investment contributions or amounts of investment returns for various types of financial transactions, including loans and bonds. Introduction to the mathematics of modern financial analysis, including calculations involving yield curves, spot rates, forward rates, duration, convexity, and immunization and short sales; introduction to financial derivatives, (forwards, options, futures, swaps) and their use in risk management; and introduction to the concept of no-arbitrage as a fundamental concept in financial mathematics.
Introduction to stochastic processes and their applications in actuarial science. Includes discrete-time and continuous-time processes. Markov chains, the Poisson process, compound Poisson processes, non-homogeneous Poisson processes, arithmetic and geometric Brownian motions, and applications of theses processes in computation of resident fees for continuing care retirement communities, and pricing of financial instruments.
Prereq: ACTS 440/840 and STAT 462, both with a grade of "C" or better.
First course of the sequence of two on the theory and applications of contingency mathematics in the areas of life and health insurance, annuities, and pensions. Probabilistic models are emphasized.
Prereq: ACTS 470/870 and STAT 462, both with a grade of "C" or better.
Life insurance reserve for models based on a single life. Introduction to multiple life models for pensions and life insurance and to multiple decrement models.
Prereq: STAT 462 with a grade of "C" or better.
Applications of compound distributions in modeling of insurance loss, continuous-time compound Poisson surplus processes, computation of ruin probabilities, the distributions of the deficit at the time of ruin and the maximal aggregate loss, the effect of reinsurance on the probability of ruin.
Prereq: ACTS 471/871 and FINA 307/307H or 338.
Principles and practices of pricing/funding and valuation for life, health and property and liability insurance, annuities and pension plans. Commercially available actuarial modeling software used for illustration.
Special Topics in Actuarial Science
Prereq: ACTS 870 with a grade of "C" or better.
Basic theory of pension mathematics. Funding methods, unit credit, entry age normal, aggregate cost, actuarial assumptions, tax deductible contributisno, multi-employer pension plans, deposit administration dividend formulas, variable annuities, and ERISA.
Prereq: Permission
Prereq: ACTS 870 with a grade of “C” or better.
Advanced topics in actuarial theory including Utility Theory, Risk Theory, and Ruin Theory, and their applications.
Prereq: STAT 883 with a grade of "C" or better.
Introduction to sigma-fields and information structures, the Riemann integral, the Riemann Stieltjes integral, the Lebesque integral, conditional expectation, martingales, Brownian motion, the Ito integral and Ito calculus, equilibrium price measures, and the Black-Scholes option pricing mod
