Math Finance

• QST MF 840: Data Analysis and Financial Econometrics
  This is the second course of the econometrics sequence in the Mathematical Finance program. The course quickly reviews OLS, GLS, the Maximum Likelihood principle (MLE). Then, the core of the course concentrates on Bayesian Inference, now an unavoidable mainstay of Financial Econometrics. After learning the principles of Bayesian Inference, we study their implementation for key models in finance, especially related to portfolio design and volatility forecasting. We also briefly discuss the Lasso and Ridge methods, and contrast them with the Bayesian approach Over the last twenty years, radical developments in simulation methods, such as Markov Chain Monte Carlo (MCMC) have extended the capabilities of Bayesian methods. Therefore, after studying direct Monte Carlo simulation methods, the course covers non- trivial methods of simulation such as Markov Chain Monte Carlo (MCMC), applying them to implement models such as stochastic volatility. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 850: Advanced Computational Methods
  This course explores algorithmic and numerical schemes used in practice for the pricing and hedging of financial derivative products. The focus of this course lies on data analysis. It covers such topics as: stochastic models with jumps, advanced simulation methods, optimization routines, and tree- based approaches. It also introduces machine learning concepts and methodologies, including cross validation, dimensionality reduction, random forests, neural networks, clustering, and support vector machines. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 921: Topics in Dynamic Asset Pricing
  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. Particular emphasis will be placed on (i) consumption-portfolio choice problems and (ii) equilibrium asset pricing models. Advances involving non-separable preferences, incomplete information and heterogeneous agents will be discussed. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 922: Advanced Mathematical Finance
  Provides a rigorous introduction to the modern theory of stochastic calculus, with a particular emphasis on continuous time, continuous path stochastic processes; the canonical example being Brownian motion. The main topics covered include basic definitions relating to stochastic processes: filtrations; measurability; stopping times; cadlag processes; Martingales; quadratic variation, etc.; the fundamental inequalities, convergence results, optional sampling theorem, and other properties of Martingales; the Doob-Meyer decomposition; construction of local Martingales; the analysis of the space of continuous square integrable Martingales; the definition and construction of Brownian motion: the Kolmogorov-Daniell consistency theorem, the Kolmogorov-Centsov theorem on continuous modifications; the construction of Wiener measure; analysis of Brownian motion: Markov, strong Markov properties; path regularity and distributional properties; the construction of the stochastic integral with respect to a continuous Martingale; Ito's change of variable formula; representation results; Girsanov's theorem; local time of Brownian motion; and Stochastic differential equations and diffusions: construction of strong and weak solutions; the Martingale problem; connections with partial differential equations and harmonic analysis; the Feynman-Kac formula.
• QST MF 930: Advanced Corporate Finance
  This doctoral level class on corporate finance covers both theoretical and empirical work. Rather than explaining the underpinnings of basic corporate research (e.g., model/applications dealing with asymmetric information, agency problems, and capital market frictions), we go deeper in understanding "how to operationalize" research on concrete topics that are central to contemporary corporate finance, such as bankruptcy, capital structure, mergers and acquisitions, the firm boundaries, investment, and much more. The class also looks at the interface between corporate finance and other research areas, such as asset pricing and banking. The course is a blend of new approaches to modeling in corporate research (e.g., dynamic, structural models of financial policy that generate typically quantitative predictions) and new approaches to testing design (e.g., regression discontinuities and natural experiments). The goal is to expose the students to the "state-of-the-art" of research in corporate finance and prepare them to do research in corporate finance using new methods and tools. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 990: Current Topics Seminar
  For PhD students in the Mathematical Finance program. Registered by permission only.
• QST MF 998: Directed Study: Mathematical Finance
  PhD-level directed study in Mathematical Finance. 1, 2, or 3 cr. Application available on the Graduate Center website.
• QST MF 999: Directed Study: Mathematical Finance
  PhD-level directed study in Mathematical Finance. 1, 2, or 3 cr. Application available on the Graduate Center website.

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