Technology and Algorithmic Finance Track

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The topics are integration, series of real numbers, sequences and series of functions and Fourier series. Important concepts and theorems include Riemann and Riemann-Stieltjes integral, fundamental theorem of calculus, the mean value theorem of integrals, Dirichlet test, absolute and conditional convergence, uniform convergence, Weierstrass test, power series, orthogonal functions and Fourier series.

Topics covered are basic concepts of linear algebra continuing with: Differentiation and integration for vector-valued functions of one and several variables: Measure theory and Lebesgue integration on the Euclidean space.

Introduction to abstract measure theory and integration. This course will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments form an essential part of the course.

The course will introduce students to numerical methods for 1 nonlinear equations, Newton's method; 2 ordinary differential equations, Runge-Kutta algorithmic trading and quantitative strategies nyu multistep methods, convergence and stability; 3 finite difference, finite element and integral equation methods for elliptic partial differential equations; 4 fast solvers, multigrid methods; and 5 parabolic and hyperbolic partial differential equations.

Classics in Applied Mathematics [Series]. Society for Industrial and Applied Mathematics. It covers software and algorithmic tools necessary to practical numerical calculation for modern quantitative finance.

Linear dependence, linear independence; span, basis, dimension, isomorphism. Linear functionals, dual spaces. Linear mappings, null space, range, fundamental theorem of linear algebra.

Underdetermined systems of linear equations. Composition, inverse, transpose of linear maps, algebra of linear maps. Eigenvalue problem, eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem. Pure and Applied Algorithmic trading and quantitative strategies nyu Linear Algebra and Its Applications 2 nd ed.

Trace, determinant, characteristic and minimal polynomial. Eigenvalues, diagonalization, spectral theorem and spectral mapping theorem. Polar and singular value decomposition. Intro to matrix Lie algebras and Lie groups. Linear Algebra 4 th ed.

Upper Saddle River, NJ: Representations of finite groups. Characters, orthogonality of characters of irreducible representations, a ring of representations. Representations of compact groups and the Peter-Weyl theorem.

Lie groups, examples of Lie groups, representations and characters of Algorithmic trading and quantitative strategies nyu group. Lie algebras associated algorithmic trading and quantitative strategies nyu Lie groups. Applications of the group representations in algebra and physics. Elements of algebraic geometry.

This graduate course aims at covering several fundamental constructions in Algebraic geometry, from the point of view of a first course in scheme theory.

Undergraduate elementary number theory, abstract algebra, including groups, rings and ideals, fields, and Galois theory e. Homology and cohomology from simplicial, singular, cellular, axiomatic and differential form viewpoints. Axiomatic characterizations and applications to geometrical problems of embedding and fixed points. Products and ring structures. Vector bundles, tangent bundles, DeRham cohomology and differential forms. Differential Geometry II will focus on Riemannian geometry. Topics to be covered may include: The course will be concerned with Ricci curvature including almost rigidity and structure of Gromov-Hausdorff limit spaces.

Some Riemannian geometry, algebraic algorithmic trading and quantitative strategies nyu, and group theory. Some familiarity with Lie groups may be helpful. Geometric group theory is based on studying discrete groups by looking at geometric objects on which they act.

A single group can act on many different spaces, but all of these spaces share certain large-scale geometric properties and asymptotic behavior. This is a broad field, so we will study an assortment of topics, possibly including: The fundamental theorem of algebra, the argument principle; calculus of residues, Fourier transform; the Gamma and Zeta functions, product expansions; Schwarz principle of reflection and Schwarz-Christoffel transformation; elliptic functions, Riemann surfaces; conformal mapping and univalent functions; maximum principle and Schwarz's algorithmic trading and quantitative strategies nyu the Riemann mapping theorem.

Complex Analysis 3 rd ed. Existence and uniqueness of initial value problems. Boundary value problems and Sturm-Liouville theory. Comparison theorem for second order equations. Asymptotic behavior of nonlinear systems. Graduate Studies in Mathematics [Series, Vol. Ordinary Differential Equations and Dynamical Systems. The course gives an introduction to Sobolev spaces, Holder spaces, and the theory of distributions; elliptic equations, harmonic functions, algorithmic trading and quantitative strategies nyu value problems, regularity of solutions, Hilbert space methods, eigenvalue problems; general hyperbolic systems, initial value problems, energy methods; linear evaluation equations, Fourier methods for solving initial value problems, parabolic equations, dispersive equations; nonlinear elliptic problems, variational methods; Navier-Stokes and Euler equations.

Topics in real variable methods: Introduction algorithmic trading and quantitative strategies nyu Littlewood-Paley theory, time-frequency analysis, and wavelet theory. Classical and Multilinear Harmonic Analysis Vol. Variational Methods And Gamma-Convergence. This course will review the basics of algorithmic trading and quantitative strategies nyu variational problems and their associated PDEs, and present the notion of Gamma-convergence used for analyzing asymptotics of variational problems.

It will emphasize general algorithmic trading and quantitative strategies nyu as well as a diversity of examples. A rough outline includes: Struwe; Direct methods in the calculus of variations, B. DaCorogna, Modern Methods in the calculus of variations, I.

Leoni, Gamma-convergence for Beginners, A. Braides, Conservation laws and moving frames, F. In this course we will show how to analyze invariant random matrix ensembles using Riemann-Hilbert methods.

The main goal will be to prove universality for such ensembles. This course is an introduction to ergodic theory, a probabilistic approach to dynamical systems. No prior knowledge of the subject is assumed. Topics include ergodicity, the Ergodic Theorems, mixing properties, entropy; ergodic theory of continuous and differentiable maps including Lyapunov exponents.

Graduate Texts in Mathematics [Series, Bk. An Introduction to Ergodic Theory. Strichartz estimates are L p estimates which algorithmic trading and quantitative strategies nyu dispersion for, say, a solution of the linear Schrodinger equation.

I will present different contexts where such estimates can be proved: Euclidean space, Euclidean space with a potential, flat tori, compact manifolds. The theory of these estimates is intimately tied to a number of mathematical fields: I will also sketch applications to nonlinear PDE. This is a graduate class that will introduce the major topics in stochastic analysis from an applied mathematics perspective. Topics to be covered include Markov chains, stochastic processes, stochastic differential equations, numerical algorithms, and asymptotics.

It will pay particular attention to the connection between stochastic processes and PDEs, as well as to physical principles and applications. The class will attempt to strike a balance between rigour and heuristic arguments: The target audience is PhD students in applied mathematics, who need to become familiar with the tools or use them in their research.

In this course we develop a quantitative investment and trading framework. In the first part of the course, we study the mechanics of trading in the financial markets, some typical trading strategies, and how to work with and model high frequency data.

Then we turn to transaction costs and market impact models, portfolio construction and robust optimization, and optimal betting and execution strategies. In the last part of the course, we focus on simulation techniques, back-testing strategies, and performance measurement. We use advanced econometric tools and model risk mitigation techniques throughout the course.

This course provides brief mathematical introductions to elasticity, classical mechanics, and statistical mechanics -- topics at the interface where differential equations and probability meet physics and materials science. For students preparing to do research on physical applications, the class provides an introduction to crucial concepts and tools; for students of analysis the class provides valuable context by exploring some central applications.

No prior exposure to mechanics or physics is assumed. The segment on elasticity about 6 weeks will include: The segment on classical mechanics about 5 weeks will include: The segment on statistical mechanics about 3 weeks will include basic concepts such as the microcanonical and canonical ensembles, entropy, and the equilibrium distribution; some simple examples; and the numerical method known as Metropolis sampling.

Risk Management is arguably one of the most important tools for managing a trading book and quantifying the effects of leverage and diversification or lack thereof. A systematic approach to the subject is adopted, based on selection of risk factors, econometric analysis, extreme-value theory for tail estimation, correlation analysis, and copulas to estimate joint factor distributions. We will cover the construction of risk-measures e,g.

VaR and Expected Shortfall and historical back-testing of portfolios.

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Applications include high frequency finance, behavioral finance, agent- based modeling and algorithmic trading and portfolio management. This course introduces a framework with which to understand and leverage information technology. The technology components covered include telecommunications, groupware, imaging and document processing, artificial intelligence, networks, protocols, risk, and object-oriented analysis and design.

The course examines the procedures and market conventions for processing, verifying, and confirming completed transactions; resolving conflicts; decisions involved in developing clearing operations or purchasing clearing services; the role played by clearing houses; and numerous issues associated with cross-border transactions. The course also examines the effects of transaction processing, liquidity management, organizational structure, and personnel and compliance on the nature of operational risk.

Qualitative and quantitative measures of operational risk are discussed. This course prepares students to research and practice in this area by providing the tools and techniques to generate and evaluate individual trading strategies, combine them into a coherent portfolio, manage the resulting risks, and monitor for excess deviations from expected performance. It introduces theoretical concepts such as cointegration, risk capital allocation, proper backtesting, and factor analysis, as well as practical considerations such as data mining, automated systems, and trade execution.

Student teams will prepare and present projects or case studies applying hte concepts covered in class. As such it covers fundamental concepts such as financial database design, use, and maintenance, distributed financial computing and associated storage, grid and cloud computing, modeling unstructured financial data, and data mining for risk management.

The goal of this course is to survey several algorithmic strategies used by financial institutions and to understand their implementation in the context of order management systems and standard financial protocols such as FIX and FIXatdl. Student teams will prepare and present projects or case studies applying the concepts covered in class. This course introduces the tools and techniques of analyzing news, how to quantify textual items based on, for example, positive or negative sentiment, relevance to each stock, and the amount of novelty in the content.

Applications to trading strategies are discussed, including both absolute and relative return strategies, and risk management strategies. Students will be exposed to leading software in this cutting-edge space.

Selected topics are emphasized and provide a focus for further study. Portfolio robustness and extreme markets and moral hazard; data-mining biases and decision error; and decision-making with incomplete information. These techniques are analyzed both mathematically and using computer aided software that allows for the solution and the handling of such problems. In addition, the course introduces techniques for Monte Carlo simulation techniques and their use to deal with theoretically complex financial products in a tractable and practical manner.

Both self-writing of software as well as using outstanding computer programs routinely used in financial and insurance industries will be used. Such biased behavior can lead to market inefficiencies, market opportunities and market failure. After a brief introduction to the topic and its research history, the course focuses on the limits to arbitrage created by decision bias, the equity premium puzzle, market over-reaction and under-reaction.

The course seeks to understand how and where opportunities for and threats to wealth accumulation exist as a result of the mismatch between investor behavior and the algorithmic assumptions about investment behavior inherent in financial theory. The focus is on the principles and practice of financial engineering and risk management and on developing intuition: The goal is to prepare you to be able to evaluate an arbitrary derivative given only its term sheet.

To that end, the course requires a project almost every week. Projects can be done in any programming language Excel, Mathematica, R, Python, etc. The primary prerequisite is familiarity with standard option pricing and Greeks. A portion of the final exam may involve a live computation project. The course emphasizes backtesting and risk factor analysis as well as optimization to reduce tracking error.

It will also address how a quantitative investment approach can help both individual and institutional investors make sound long-term investment decisions. Selected topics are emphasized and provide focus for further study. Course topics may include for example: Examples can include urban finance engineering, environmental finance, infrastructure and projects finance, real-estate finance, insurance finance and derivatives, and macro hedge funds management. Topics covered include financial time series analysis, advanced risk tools, applied econometrics, portfolio management, and derivatives valuation.

Students will be required to write some code in R every week. Facebook Twitter Instagram YouTube. Preview The New Tandon Website! Graduate Standing 3 Courses from the Following: The following are recommended labs for this track: Financial Markets and Corporate Finance Track: Technology and Algorithmic Finance Track: