# Courses

## Past PhD in Mathematical Finance Courses

#### EC701: Microeconomic Theory

Neoclassical general equilibrium theory. Topics covered include consumption, production, existence of competitive equilibrium, fundamental welfare theorems, externalities, and uncertainty.

#### EC702: Macroeconomic Theory

Basic Keynesian model: consumption, investment, and money demand functions. Extension to the open economy. Determinants of money supply. Effectiveness of monetary and fiscal policy. Inflation and income policy. Elementary growth models.

#### EC703: Advanced Microeconomic Theory I

Walrasian equilibrium: existence, uniqueness and core equivalence. Uncertainty: Arrow Debreu contingent commodities, Radner equilibrium, incomplete markets. Economics of information: rational expectations, adverse selection, signaling and screening. The principal-agent problem.

#### EC704: Advanced Macroeconomic Theory II

Consumption theory and evidence; investment theory and evidence; monetary theory; micro foundations of macro systems; theory of rational expectations; models of fiscal and monetary macroeconomic policy; and employment theory and policy.

#### EC712: Time Series Econometrics

Presents standard theory of stationary processes: models, estimation in the time and frequency domain, spectral analysis, asymptotic distribution, Kalman filter; VAR models. Also deals with non-stationary processes and discusses topics such as: functional central limit theorem, asymptotic results with unit roots, tests for unit roots, estimation and test in cointegrated systems and models with structural changes.

#### EC716: Game Theory

Introduction to noncooperative and cooperative games with applications in the social sciences.

#### EC744: Economic Dynamics

Introduces the theory and application of dynamic optimization and equilibrium analysis, with emphasis on computational methods and techniques. Covers discrete and continuous time models in both deterministic and stochastic environments.

#### EC745: Macroeconomics and Financial Markets

For second- and third-year PhD students. Topics and approaches combine macroeconomics and finance, with an emphasis on developing and testing theories that involve linkages between financial markets and the macro economy.

#### EC794: Financial Econometrics

For PhD students working in the area of econometrics, finance, and applied macroeconomics. Topics include prediction of asset returns, financial volatility, asset allocation, value at risk, and high frequency data analysis.

#### FE918: Doctoral Seminar in Finance

This doctoral course, is designed to provide students with an introduction to financial economics. This lecture-based course will cover no arbitrage conditions, preferences and risk aversion, portfolio selection, the capital asset pricing model, asset pricing and dynamic asset pricing. In addition to lectures, this class will include readings and assignments. Open to MBA students with faculty member’s permission. Must have strong quantitative background and several courses in finance or economics.

#### FE919: Derivative Securities

This course provides a comprehensive and in-depth treatment of valuation methods for derivatives securities. Extensive use is made of continuous time stochastic processes, stochastic calculus and martingale methods. The main topics to be addressed include 1) European contingent claims valuation, 2) American claims, 3) valuation in the standard model, 4) barrier options, 5) numerical methods for ingle asset derivatives, and 6) multi-asset options. Additional topics may be covered depending on time constraints.

#### FE920: Advanced Capital Markets

This course provides a comprehensive and in-depth treatment of modern asset pricing theories. Extensive use is made of continuous time stochastic processes, stochastic calculus and optimal control. In particular, martingale methods are employed to address the following topics: (i) optimal consumption-portfolio policies and (ii) asset pricing in general equilibrium models. Recent advances involving nonseparable preferences, incomplete information, incomplete markets, constraints and agents diversity will be discussed.

#### MA711: Real Analysis

Measure theory and integration on measure spaces, specialization to integration on locally compact spaces, and the Haar integral. Lp spaces, duality, and representation theorems. Introduction to Banach and Hilbert spaces, open mapping theorem, spectral theorem for Hermitian operators, and compact and Fredholm operators.

#### MA717: Functional Analysis I

Theory of Banach and Hilbert spaces, and Hahn-Banach and separation theorems. Dual spaces. Banach contraction mapping theorem. Reflexivity and Krein-Milman theorem. Operator theory. Brouwer-Schauder fixed-point theorems. Applications to probability, dynamical systems, and applied mathematics.

#### MA783

Proof–based approach to stochastic processes. Brownian motion. Continuous martingales. Stochastic integration. Itô formula. Girsanov’s Theorem. Stochastic differential equations. Feynman–Kac formula. Markov Processes. Local times. Lévy processes. Semimartingales and the general stochastic integral. Stable processes. Fractional Brownian motion.

#### MF772: Credit Risk

This course covers asset pricing models (preferences, utility functions, risk aversion, basic consumption model, the mean-variance frontier, factor models, and robust preferences); and options pricing and risk management (arbitrage pricing in a complete market, delta-hedging, risk measure, and value-at-Risk).