Topics in Mathematics with Applications in Finance

This is a guest lecture on quanto credit hedging, including using mathematical models in trading.

This lecture is an introduction to counterparty credit risk, featuring credit valuation as well as the broad economic objectives of a financial institution. It also concludes the course.

This is a guest lecture that describes the HJM model for interest rates and credit, including hedging risk on interest and credit rate derivatives.

This guest lecture features the Ross Recovery Theorem.

This lecture covers the topic of stochastic differential equations, linking probablity theory with ordinary and partial differential equations.

This guest lecture focuses on option price and probability duality.

This is a lecture on risk-neutral pricing, featuring the Black-Scholes formula and risk-neutral valuation.

This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.

This lecture explains the theory behind Itō calculus.

This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion.

This lecture describes factor modeling, featuring linear, macroeconomic, fundamental, and statistical factor models, and principal components analysis.

This lecture describes portfolio theory, including topics of Marowitz mean-variance optimization, von Neumann-Morganstern utility theory, portfolio optimization constraints, and risk measures.

This is the last of three lectures introducing the topic of time series analysis, describing cointegration, cointegrated VAR models, linear state-space models, and Kalman filters.

This is a guest lecture on commodity modeling, analyzing the methods of generating profit with a constrained system.

This is the second of three lectures introducing the topic of time series analysis, describing multivariate time series, representation theorems, and least-squares estimation.

This is a guest lecture on regularized pricing and risk models, featuring explanations of bonds, swaps, and yield curve models.

This lecture introduces the topic of volatility modeling, including historical volatility, geometric Brownian motion, and Poisson jump diffusions.

This is the first of three lectures introducing the topic of time series analysis, describing stochastic processes by applying regression and stationarity models.

This lecture introduces the mathematical and statistical foundations of regression analysis, particularly linear regression.

This is an applications lecture on Value At Risk (VAR) models, and how financial institutions manage market risk.

This lecture introduces stochastic processes, including random walks and Markov chains.

This lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem.

This lecture is a review of the linear algebra needed for the course, including matrices, linear transformations, eigenvalue, and eigenvectors.

In the first lecture of this course, the instructors introduce key terms and concepts related to financial products, markets, and quantitative analysis.