M.S.E. Operations Research and Financial Engineering

FIN 501 Asset Pricing I: Pricing Models and Derivatives (also

ORF 514

) Provides and introduction ot the mofern theory of asset pricing. Topics include: (1) no arbitrage, Arrow-Debreu prices and equivalent martingale measure; (ii) security structure and market completeness; (iii) mean-variance analysis, Beta-Pricing, CAPM; and (iv) introduction to derivative pricing.

ORF 504 Financial Econometrics (also

FIN 504

) This course covers econometric and statistical methods as applied to finance. Topics include: (i) Measurement issues in finance (ii) Predictability of asset returns and volatilities (iii) Value at Risk and extremal events (iv) Linear factor pricing and portfolio problems (v) Intertemporal models of the Stochastic Discount Factor and Generalized Method of Moments (vi) Vector Autoregressive and maximum likelihood methods in finance (vii) Risk Neutral valuation in discrete time (viii) Estimation methods for continuous time models (ix) Volatility smiles and alternatives to Black-Scholes (x) Nonparametric statistical methods for option pricing.

ORF 505 Statistical Analysis of Financial Data (also

FIN 505

) Linear and mixed effect models. Nonlinear regression. Nonparametricegression and classification. Time series analysis: stationarity and classical linear models (AR, MA, ARMA, ..). Nonlinear and nonstationary time series models. State space systems, hidden Markov models and filtering.

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. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 one semester prior to taking the general examination.

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 one semester prior to taking the general examination.

ORF 511 Extramural Summer Project 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 Asset Pricing II: Stochastic Calculus and Advanced Derivatives (also

FIN 503

) Course begins with an overview of basic probability theory and covers the elements of stochastic calculus and stochastic differential equations that are widely used in modern financial applications. Topics include the Poisson process, Brownian motion, martingales, diffusions and their connection with partial differential equations. Examples from applications include the Black-Scholes option pricing and hedging theory, bond pricing and stochastic volatility models.

ORF 522 Linear and Nonlinear Optimization Theoretical concepts underlying linear programming, with computer implementations of some of the different methods. The topics covered include duality theory, the simplex method, interior point methods, related numerical issues, and modeling paradigms.

ORF 523 Convex and Conic Optimization An introduction to the central concepts needed for studying the theory, algorithms, and applications of nonlinear optimization problems. Topics covered include first- and second-order optimality conditions; unconstrained methods, including steepest descent, conjugate gradient, and quasi-Newtonian methods; constrained active-set methods; and duality theory and Lagrangian methods. Prerequisite: linear optimization.

ORF 524 Statistical Theory and Methods A graduate level introduction to statistical theory and methods. It introduces some of the most important and commonly-used principles of statistical inference and covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing, and the applications of the fundamental theory to linear models and categorical data.

ORF 525 Statistical Learning and Nonparametric Estimation An introduction to the most important and broadly utilized statistical methods used in many scienti¿c data analysis, including general linear, mixed-e¿ects, generalized linear models, regression and ANOVA models. The methodological power of statistics will be emphasized. Objectives of this course are to give students a solid understanding of these methods, and o¿er them experience in applying these methods to real data using statistical computing packages and interpreting results. For master's/Ph.D. students and advanced undergraduates.

ORF 526 Probability Theory 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, martin- gales, Markov chains, and Poisson processes.

ORF 527 Stochastic Calculus An introduction to stochastic analysis based on Brownian motion. Topics include local martingales, the Ito integral and calculus, stochastic differential equations, the Feynman-Kac formula, representation theorems, Girsanov theory, and applications in finance.

ORF 531 Computational Finance in C++ (also

FIN 531

) 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 534 Quantitative Investment Management (also

FIN 534

) A survey of central topics in the area of financial engineering and multiperiod financial planning systems. Pricing methodologies integrated with financial planning systems. Linking asset and liability strategies to maximize surplus-wealth over time. We model the organization as a multistage stochastic program with decision strategies.

ORF 535 Financial Risk Management (also

FIN 535

) This course is about measuring, modeling and managing financial risks. It introduces the variety of instruments that are used to this effect and the methods of designing and evaluating such instruments. Topics covered include risk diversification, planning models, market and nonmarket risks, and portfolio effects. Lectures meet concurrently with ORF 435. Credit for graduate course requires completion of additional assignments.

ORF 538 PDE Methods for Financial Mathematics 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-Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution.

ORF 542 Stochastic Optimal Control Deterministic optimal control, dynamic programming, and Pontryagin maximum principle. Controlled diffusion processes and stochastic dynamic programming. Hamilton-Jacobi-Bellman equation, viscosity solutions. Merton problem, singular optimal control, option pricing via utility maximization.

ORF 544 Stochastic Optimization This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such as reinforcement learning and approximate dynamic programming. Also covered are both offline and online learning problems. Considerable emphasis is placed on modeling and computation.

ORF 550 Topics in Probability (also

APC 550

) An introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. Emphasis is on developing a common set of tools that has proved to be useful in different areas. Topics may include: concentration of measure; functional, transportation cost, martingale inequalities; isoperimetry; Markov semigroups, mixing times, random fields; hypercontractivity; thresholds and influences; Stein's method; suprema of random processes; Gaussian and Rademacher inequalities; generic chaining; entropy and combinatorial dimensions; selected applications.

ORF 554 Markov Processes 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 566 High Dimensional Statistics Course is on statistical theory and methods for high-dimensional statistical learning and inferences arising from processing massive data from various scientific disciplines. Emphasis is given to penalized likelihood methods, independence screening, large covariance modeling, and large-scale hypothesis testing. The important theoretical results are proved.

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 (also

ELE 578

) Advanced topics in statistics and operations research or the investigation of problems of current interest.

ORF 574 Special Topics in Investment Science (also

FIN 574

) 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.