Mathematical Finance

• QST MF 821: Algorithmic and High-Frequency Trading
  This course will introduce concepts of electronic markets, and statistical and optimal control techniques to model and trade in these markets. We will begin with a description of the basic elements of electronic markets, some of the features of the data, its empirical implications and simple microeconomic models. Next, we will study statistical tools to estimate and predict price and volatility of the high-frequency price. Then we will investigate algorithmic trading problems from the stochastic optimal control perspective, including the optimal execution problem and show how to modify the classical approaches to include order-flow information and the effect that dark pools have on trading. Trading pairs of assets that mean-revert is another important algorithmic strategy, and we will see how stochastic control methods can be utilized to inform agents how to optimally trade. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 825: Advanced Topics in Investments
  This course is designed for students seeking to work as quants in a quantitative finance investments group. It covers utility theory, portfolio optimization, asset pricing, and some aspects of factor models, incorporating the impact of parameter uncertainty. The course does not cover risk management or fixed income instruments, nor does it describe how the financial services industry works. Rather, it teaches how a quant should optimize a portfolio. The course makes extensive use of R (Excel or VBA are not substitutes), optimization theory, statistics, regression theory (OLS, GLS, testing theory), and matrix algebra. Students should be very comfortable with these concepts before taking the course; further, students should already have taken a finance course covering expected returns models (CAPM), options and futures. The course emphasizes the ability to prove theoretical results and their validity, an essential trait for investments quants. Students who completed QST FE825 may not take this course for credit. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• 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) stochastic calculus with jumps; (ii) asset pricing models with jumps; (iii) the Hamilton-Jacobi-Bellman equation and stochastic control; (iv) numerical methods for stochastic control problems in finance. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)
• QST MF 922: Advanced Mathematical Finance
  This course provides a rigorous introduction to the modern theory of mathematical finance in incomplete markets. The first part of the course covers the fundamental theorem of asset pricing, as well as super-hedging of contingent claims, in full generality for discrete time models. The second half of the class focuses on optimal investment, pricing and hedging in continuous time incomplete markets. Here, lectures will cover optimal investment and duality for general semi-martingale models; and portfolio optimization and pricing in Markovian factor models, non-Markovian Brownian models, models with trading constraints, and models with transactions costs. Throughout this half, lectures will highlight connections to the dynamic programming principle, the Martingale optimality principle, semi-linear Cauchy partial differential equations, backward stochastic differential equations, and the theory of viscosity solutions.
• 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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