Another part of the course is concerned with the Monte Carlo methods. ![]() Examples include the generalized Black- Scholes PDE for pricing European, American and Asian options. Convergence and stability of explicit and implicit numerical schemes is analyzed. This course starts with the introduction to numerical methods for solving differential equations of evolution, including the Partial Differential Equations (PDEs) of parabolic type. Examples and data from financial applications will be used to motivate and illustrate the methods. These include linear and non-linear regression, nonparametric and semi-parametric regression, selected topics on the analysis of multivariate data and dimension-reduction, and time series analysis. This course will cover basic topics involved in modeling and analysis of financial data. Stats 509 (3 cr): Statistical Analysis of Financial Data.This is a good complement to Math 574.rallel, or Math 506 precedes Math 574. This course also demonstrates the use of Stochastic Control in the problems of Optimal Investment and Optimal Execution. In particular, it shows how Stochastic Analysis is applied to problems arising in Equity Derivatives, Foreign Exchange, Fixed Income and Credit Risk markets. A strong emphasis is made on applications of the developed methods to the problems of Mathematical Modeling in Finance. This course covers such topics as: Stochastic Integration and Stochastic Differential Equations, Change of Measure, advanced Martingale Theory and Brownian Motion, Levy processes, and Stochastic Control. Math 506 (3 cr): Stochastic Analysis of Finance.Although Math 506 is not a prerequisite for Math 574, it is strongly recommended that either these courses are taken in parallel, or Math 506 precedes Math 574. In addition, this course discusses Optimal Investment in Continuous time (Merton’s problem), High-frequency Trading (Optimal Execution), and Risk Management (e.g. These problems include pricing and hedging of (basic and exotic) Derivatives in Equity, Foreign Exchange, Fixed Income and Credit Risk markets. The course starts with the general Theory of Asset Pricing and Hedging in continuous time and then proceeds to specific problems of Mathematical Modeling in Continuous-time Finance. This course discusses Mathematical Theory of Continuous-time Finance. Math 574 (3 cr): Advanced Financial Mathematics II.Applications and real data analysis are emphasized, with students using the computer to perform statistical analyses. Topics include linear models, model fitting, identifiability, collinearity, Gauss-Markov theorem, variable selection, transformation, diagnostics, outliers and influential observations, ANOVA and ANCOVA, and common designs. This course introduces the essentials of linear models. ![]()
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