Mathematical Methods for Quantitative Finance

This module covers fundamental concepts of probability in financial mathematics, including probability laws, common distributions, Central Limit Theorem, Law of Large Numbers, characteristic functions, and asymptotic behavior. Students learn essential probabilistic tools for analyzing financial data and modeling financial phenomena.

This module focuses on statistical inference and hypothesis testing in financial contexts. Students learn regression methods and time series tests for econometric analysis, enabling them to analyze financial data and make evidence-based decisions.

This module explores various time series models including random walks, Markov processes, and GARCH models. Students learn about recursive calculations, linear time series properties, first-passage properties, and their applications to forecasting and trading strategies.

This module covers continuous time limits of discrete processes, Brownian motion properties, Itô calculus, and solving differential equations in finance. Applications focus on derivative pricing and risk management techniques.

This module examines linear algebra concepts in financial contexts, including operations on linear spaces, covariance and correlation matrices, and their applications to asset pricing. Students learn how to apply linear algebra techniques to solve financial problems.

This module covers various optimization techniques including Lagrange multipliers, quadratic programming, Markov decision processes, dynamic programming, and variational methods. Applications focus on portfolio construction, algorithmic trading, and execution optimization.

This module focuses on computational techniques in quantitative finance, with emphasis on Monte Carlo methods and quadratic programming. Students learn how to implement numerical solutions for complex financial problems.