Applied Mathematics and Statistics
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Applied Mathematics and Statistics |
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Master of Science in Applied Mathematics: Quantitative Finance Areas of Interest: Quantitative Strategy, High Frequency Trading, Fixed Income, Risk Management Graduation Date: May 25, 2011 |
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Rahul Prakash received his undergraduate degree in physics from Banaras Hindu University (BHU), Varanasi and Indian Institute of Technology (IIT), Madras. Then attended graduate school for MS (Engg.) in Computer Science from Supercomputer Education and Research Center of Indian Institute of Science (IISc), Bangalore. |
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Rahul initially worked in Bangalore for a software services company as developer and then moved to an analytics software development, where he designed and developed statistical algorithms for ARCH, GARCH and CHAID model. His interest in Finance grew while working in financial services and analytics development. He has worked for statistical package, risk analysis, model and score card development applications. |
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From the master degree in Quantitative Finance, Rahul wants to develop understanding of quantitative and computing aspects of financial markets. After graduation he wants to work for an investment bank, hedge fund or financial services firm. In his spare time, Rahul enjoys jogging, swimming and table tennis. |
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Course Descriptions
AMS 510, Analytical Methods for Applied Mathematics and Statistics Review of techniques of multivariate calculus, convergence and limits, matrix analysis, vector space basics, and Lagrange multipliers. |
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AMS 511, Foundation of Quantitative Finance Introduction to capital markets, securities pricing, and modern portfolio theory, including the organization and operation of securities market, the Efficient Market Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing Theory, and more general factor models. Common stocks and their valuation, statistical analysis, and portfolio selection in a single-period, mean-variance context will be explored along with its solution as a quadratic program. Fixed income securities and their valuation, statistical analysis, and portfolio selection. Discussion of the development and use of financial derivatives. Introduction to risk neutral pricing, stochastic calculus, and the Black-Scholes Formula. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned. |
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AMS 512, Capital Markets and Portfolio Theory Development of capital markets and portfolio theory in both continuous time and multi-period settings. Utility theory and its application to the determination of optimal consumption and investment policies. Asymptotic growth under conditions of uncertainty. Applications to problems in strategic asset allocation over finite horizons and to problems in public finance. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned. |
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AMS 514, Computational Finance Review of foundations: stochastic calculus, martingales, pricing, and arbitrage. Basic principles of Monte Carlo and the efficiency and effectiveness of simulation estimators. Generation of pseudo- and quasi-random numbers with sampling methods and distributions. Variance reduction techniques such as control variates, antithetic variates, stratified and Latin hypercube sampling, and importance sampling. Discretization methods including first and second order methods, trees, jumps, and barrier crossings. Applications in pricing American options, interest rate sensitive derivatives, mortgage-backed securities and risk management. Whenever practical, examples will use real market data. Extensive numerical exercises and projects in a general programming environment will also be assigned. |
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AMS 515, Case Studies in Computational Finance Actual applications of Quantitative Finance to problems of risk assessment, product design, portfolio management, and securities pricing will be covered. Particular attention will be paid to data collection and analysis, the design and implementation of software, and, most importantly, to differences that occur between theory and practice in model application, and to the development of practical strategies for handling cases in which model failure makes the naive use of quantitative techniques dangerous. Extensive use of guest lecturers drawn from the industry will be made. |
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AMS 517, Quantitative Risk Management The course will cover structural and reduced-form approach to pricing credit default, Markovian models (or rating-based) pricing methods, statistical inference of relative risks, counting process, correlated (or dependent) default times, copula methods and pricing models for CDOs. |
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AMS 545, Computational Geometry Study of the fundamental algorithmic problems associated with geometric computations, including convex hulls, Voronoi diagrams, triangulation, intersection, range queries, visibility, arrangements, and motion planning for robotics. Algorithmic methods include plane sweep, incremental insertion, randomization, divide-and-conquer, etc. |
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AMS 550, Stochastic Models Includes Poisson processes, renewal theory, discrete-time and continuous-time Markov processes, Brownian motion, martingales, applications to queues, statistics, and other problems of engineering and social sciences. |
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AMS 553, Simulation and Modeling A comprehensive course in formulation, implementation, and application of simulation models. Topics include data structures, simulation languages, statistical analysis, pseudorandom number generation, and design of simulation experiments. Students apply simulation modeling methods to problems of their own design. |
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AMS 570, Introduction to Mathematical Statistics Probability and distributions; multivariate distributions; distributions of functions of random variables; sampling distributions; limiting distributions; point estimation; confidence intervals; sufficient statistics; Bayesian estimation; maximum likelihood estimation; statistical tests. |
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AMS 578, Regression Theory Classical least-squares theory for regression including the Gauss-Markov theorem and classical normal statistical theory. An introduction to stepwise regression, procedures, and exploratory data analysis techniques. Analysis of variance problems as a subject of regression. Brief discussions of robustness of estimation and robustness of design. |
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AMS 595, Fundamentals of Computing Introduction to UNIX operating system, C language, graphics, and parallel supercomputing. |
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Email: rahul[dot]prakash[at]stonybrook[dot]edu |
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