Operations Research and Financial Engineering. Courses

Transcription

1 Operations Research and Financial Engineering Courses ORF 504/FIN 504 Financial Econometrics Professor Jianqing Fan This course covers econometric and statistical methods as applied to finance. Topics include asset returns and efficient market hypothesis, linear time series, discrete time volatility models, efficient portfolios and CAPM, multifactor pricing models, portfolio allocation and risk assessment, intertemporal equilibrium models, present value models, simulation methods for financial derivatives, and econometrics of continuous time finance. ORF 505/FIN 505 Modern Regression and Time Series Heavy tailed distributions and copulas. Simple and multiple linear regressions. Nonlinear regression. Nonparametric regression and classification. Time series analysis: stationarity and classical linear models (AR, MA, ARMA). Nonlinear and non-stationary time series models. State space systems, hidden Markov models and filtering. ORF 507 Master's Project I Under the direction of a faculty member, each student carries out a master's project, writes a report, and presents the results. Master's project I is usually taken during the fall semester of the Master of Engineering program; master's project II is taken during spring. ORF 508 Master's Project II Under the direction of a faculty member, each student carries out a master's project, writes a report, and presents the results. Master's project I is usually taken during the fall semester of the Master of Engineering program; master's project II is taken during spring. ORF 509 Directed Research I Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Directed Research I is normally taken during the first year of study. ORF 510 Directed Research II Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 in the fall term of their second year.

2 ORF 511 Extramural Summer Project Director Of Graduate Studies (DGS) Summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor, that will provide practical experience relevant to the student's course of study. Start date no earlier than June 1. A research report and sponsor's evaluation are required. ORF 515/FIN 503 Asset Pricing II: Stochastic Calculus and Advanced Derivatives Course covers the pricing and hedging of advanced derivatives, including topics such as exotic options, greeks, interest rate derivatives and credit derivatives, as well as covering the basics of stochastic calculus necessary for finance. Designed for Masters students. ORF 522 Linear and Convex Optimization Robert J. Vanderbei Topics discussed include: the simplex method and its complexity, degeneracy, duality, the revised simplex method, convex analysis, game theory, network flows, primal-dual interior point methods, first order optimality conditions, Newton's method, KKT conditions, quadratic programming, and convex optimization. A broad spectrum of applications are presented. ORF 523 Advanced Optimization Sebastien Bubeck A mathematical introduction to large-scale optimization and stochastic optimization. Topics covered include the analysis of diverse gradient-descent algorithms such as sub-gradient descent, Nesterov's accelerated gradient descent, FISTA and mirror descent, as well as a discussion of complexity lower bounds à la Nemirovski. These methods will be compared to the semi-definite programming approach and applications to high-dimensional statistics and machine learning will also be discussed. ORF 524 Statistical Theory and Methods Philippe Rigollet A graduate-level introduction to statistical theory and methods and some of the most important and commonly-used principles of statistical inference. Covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing. ORF 525 Statistical Learning and Non-Parametric Estimation Philippe Rigollet A theoretical introduction to statistical learning problems related to regression and classification. Topics covered include: Principle Component Analysis, nonparametric estimation, sparse regression, and Classification and Statistical learning ORF 526 Probability Theory Patrick Cheridito Graduate introduction to probability theory beginning with a review of measure and integration. Topics include random variables, expectation, characteristic functions, law of large numbers, central limit theorem, conditioning, martingales, Markov chains, and Poisson processes

3 ORF 527 Stochastic Calculus Ramon van Handel An introduction to stochastic calculus based on Brownian motion.topics include:construction of Brownian motion; martingales in continuous time; the Ito integral; localization; Ito calculus; stochastic differential equations; Girsanov's theorem; martingale representation; Feynman-Kac formula. ORF 531/FIN 531 Computational Finance in C++ The intent of this course is to introduce the student to the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, and to prepare the student for the development of new applications. The student will be introduced to C++, the weekly homework will involve writing C++ code, and the final project will also involve programming in the same environment. ORF 533 Convex Analysis for Mathematical Finance Tools from Convex Analysis are studied in the context of Mathematical Finance and economics, including the Hahn-Banach theorem, Legendre-Fenchel transforms, biconjugation theorem, subdifferentials, and duality. As a main application, translation invariant functions such as risk measures, no-arbitrage price bounds, good deal bounds, benefit functions and optimized certainty equivalents, are studied. Further applications include the Fundamental Theorem of Asset Pricing, hedging problems, capital/risk allocation and utility maximization. ORF 534 Quantitative Investment Science John M. Mulvey A survey of central topics in the area of investment management and financial planning. Integrating pricing methodologies with financial planning models. Linking asset and liability strategies to achieve investment goals and meet liabilities. We model the enterprise as a multi-stage stochastic program with decision strategies. ORF 535/FIN 535 Financial Risk Management This course covers the basic concepts of modeling, measuring and managing financial risks. Topics include portfolio optimization (mean variance approach and expected utility), interest rate risk, pricing and hedging in incomplete markets, indifference pricing, risk measures, systemic risk. ORF 538 PDE Methods for Financial Math Ronnie Sircar An introduction to analytical and computational methods common to financial engineering problems. Aimed at PhD students and advanced masters students who have studied stochastic calculus, the course focuses on uses of partial differential equations: their appearance in pricing financial derivatives, their connection with Markov processes, their occurrence as Hamilton-

4 Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution. ORF 542 Stochastic Control and Stochastic Differential Games Review of (forward) stochastic differential equations. Introduction to Backward Stochastic Differential Equations (BSDE's). Stochastic control=dynamic programming, HJB equations and connection with BSDE's. Stochastic differential games=nash equilibriums. Isaacs condition and BSDE's. Applications of stochastic control and stochastic games to recent research results in Finance. ORF 551/APC 551 Random Measures and Levy Processes Erhan Çinlar Poisson random measures, additive measures, Poisson-Dirichlet processes, self-exciting point processes; Levy processes, Ito-Levy characterization; subordination, subordinators, and stable processes. ORF 554 Markov Processes Erhan Çinlar Markov processes with general state spaces; transition semigroups, generators, resolvants; hitting times, jumps, and Levy systems; additive functionals and random time changes; killing and creation of Markovian motions. ORF 557 Stochastic Analysis Seminar Recent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging. ORF 558 Stochastic Analysis Seminar Recent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging. ORF 565 Empirical Processes and Asymptotic Theory Jianqing Fan Empirical Process theory mainly extends the law of large numbers (LLN), central limit theorem (CLT) and exponential inequalities to uniform LLN's and CLT's and concentration inequalities. This uniformaty is useful to statisticians and computer scientists in that they often model data as a sample from some unknown distribution and desire to estimate certain aspects of the population. Uniform LLN or CLT and concentration inequalities will imply that certain sample averages will be uniformly close to their expectations regardless of the unknown distributions. This class intends to review modern empirical process theory and its related asymptotics.

5 ORF 569 Special Topics in Statistics and Operations Research Advanced topics in statistics and operations research or the investigation of problems of current interest. ORF 570 Special Topics in Statistics and Operations Research Advanced topics in statistics and operations research or the investigation of problems of current interest. ORF 574/FIN 574 Special Topics in Investment Science John M. Mulvey Emphasis on quantitative analysis of markets, trading strategies, risk and return profiles and portfolio analysis. Students develop portfolios of hedge funds; analyze trading models for various hedge fund styles; develop Value-at-Risk analysis of various trading systems and portfolios; analyze relationship between macro-economic variables and various hedge fund trading strategies; analyze hedge funds from the standpoint of asset allocation and efficient frontier models. We will also bring in experts and practitioners in a number of hedge fund trading strategies to add industry feel and context to the lectures and exercises. ORF 575 Financial Engineering Seminar Ronnie Sircar Discussion of recent topics and papers in financial mathematics.