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Course Criteria
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0.00 - 4.00 Credits
This course measures spaces, random variables, expectation, characteristic functions, law of large numbers, central limit theorem, conditioning, Martingales, and Markov chains.
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0.00 - 4.00 Credits
An introduction to stochastic calculus based on Brownian motion.Topics include:construction of Brownian motion; martingales in continuous time; the Ito integral; localization; Ito calculus; stochastic differential equations; Girsanov's theorem; martingale representation; Feynman-Kac formula.
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0.00 - 4.00 Credits
The intent of this course is to introduce the student to the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, and to prepare the student for the development of new applications. The student will be introduced to C++, the weekly homework will involve writing C++ code, and the final project will also involve programming in the same environment.
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0.00 - 4.00 Credits
Tools from Convex Analysis are studied in the context of Mathematical Finance and economics, including the Hahn-Banach theorem, Legendre-Fenchel transforms, biconjugation theorem, subdifferentials, and duality. As a main application, translation invariant functions such as risk measures, no-arbitrage price bounds, good deal bounds, benefit functions and optimized certainty equivalents, are studied. Further applications include the Fundamental Theorem of Asset Pricing, hedging problems, capital/risk allocation and utility maximization.
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0.00 - 4.00 Credits
A survey of central topics in the area of financial engineering and multiperiod financial planning systems. Pricing methodologies integrated with financial planning models. Linking asset and liability strategies to maximize surplus-wealth over time. We model the enterprise as a multistage stochastic program with decision strategies.
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0.00 - 4.00 Credits
This course will discuss review of (forward) stochastic differential equations; Introduction to Backward Stochastic Differential Equations (BSDE); Stochastic Control: Dynamic Programming, Hamilton-Jacobi-Bellman equations and connection with BSDEs; Introduction to games and the notion of Nash equilibrium; Stochastic differential games, Isaacs condition and BSDEs
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0.00 - 4.00 Credits
This course discusses Poisson random measures, additive measures, Poisson-Dirichlet processes, self-exciting point processes; Levy processes, Ito-Levy characterization; subordination, subordinators, and stable processes.
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0.00 - 4.00 Credits
Recent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging.
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0.00 - 4.00 Credits
Algorithms for approximate dynamic programming/reinforcement learning come in a number of styles. This seminar will survey the literature on the theory supporting the convergence of different algorithms on different classes of problems drawing from computer science, engineering, economics and operations research. Each week will consist of a presentation by one of the students that offers a convergence proof for a particular algorithm/problem class.
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0.00 - 4.00 Credits
The focus of this elementary course is on sounds, letters and basic grammar of Persian language. The students will be exposed to the Persian culture through selected prose, daily news and class discussions.
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