# Topics in Mathematics with Applications in Finance

## Video Lectures

Displaying all 26 video lectures.

Lecture 1Play Video |
Introduction, Financial Terms and ConceptsIn the first lecture of this course, the instructors introduce key terms and concepts related to financial products, markets, and quantitative analysis. Instructor: Peter Kempthorne, Choongbum Lee, Vasily Strela, Jake Xia |

Lecture 2Play Video |
Linear AlgebraThis lecture is a review of the linear algebra needed for the course, including matrices, linear transformations, eigenvalue, and eigenvectors. Instructor: Choongbum Lee |

Lecture 3Play Video |
Probability TheoryThis lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem. *NOTE: Lecture 4 was not recorded. Instructor: Choongbum Lee |

Lecture 4Play Video |
Unavailable |

Lecture 5Play Video |
Stochastic Processes IInstructor: Choongbum Lee *NOTE: Lecture 4 was not recorded. This lecture introduces stochastic processes, including random walks and Markov chains. |

Lecture 6Play Video |
Regression AnalysisThis lecture introduces the mathematical and statistical foundations of regression analysis, particularly linear regression. Instructor: Peter Kempthorne |

Lecture 7Play Video |
Value At Risk (VAR) ModelsThis is an applications lecture on Value At Risk (VAR) models, and how financial institutions manage market risk. Instructor: Kenneth Abbott |

Lecture 8Play Video |
Time Series Analysis IThis is the first of three lectures introducing the topic of time series analysis, describing stochastic processes by applying regression and stationarity models. Instructor: Peter Kempthorne |

Lecture 9Play Video |
Volatility ModelingThis lecture introduces the topic of volatility modeling, including historical volatility, geometric Brownian motion, and Poisson jump diffusions. Instructor: Peter Kempthorne |

Lecture 10Play Video |
Regularized Pricing and Risk ModelsThis is a guest lecture on regularized pricing and risk models, featuring explanations of bonds, swaps, and yield curve models. Instructor: Ivan Masyukov |

Lecture 11Play Video |
Time Series Analysis IIThis is the second of three lectures introducing the topic of time series analysis, describing multivariate time series, representation theorems, and least-squares estimation. Instructor: Peter Kempthorne |

Lecture 12Play Video |
Time Series Analysis IIIThis 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. Instructor: Peter Kempthorne |

Lecture 13Play Video |
Commodity ModelsThis is a guest lecture on commodity modeling, analyzing the methods of generating profit with a constrained system. Instructor: Alexander Eydeland |

Lecture 14Play Video |
Portfolio TheoryThis lecture describes portfolio theory, including topics of Marowitz mean-variance optimization, von Neumann-Morganstern utility theory, portfolio optimization constraints, and risk measures. Instructor: Peter Kempthorne |

Lecture 15Play Video |
Factor ModelingThis lecture describes factor modeling, featuring linear, macroeconomic, fundamental, and statistical factor models, and principal components analysis. Instructor: Peter Kempthorne |

Lecture 16Play Video |
Portfolio ManagementThis lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations. Instructor: Jake Xia |

Lecture 17Play Video |
Stochastic Processes IIThis lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion. Instructor: Choongbum Lee |

Lecture 18Play Video |
Itō CalculusThis lecture explains the theory behind Itō calculus. Instructor: Choongbum Lee |

Lecture 19Play Video |
Black-Scholes Formula, Risk-neutral ValuationThis is a lecture on risk-neutral pricing, featuring the Black-Scholes formula and risk-neutral valuation. Instructor: Vasily Strela |

Lecture 20Play Video |
Option Price and Probability DualityThis guest lecture focuses on option price and probability duality. Instructor: Stephen Blythe |

Lecture 21Play Video |
Stochastic Differential EquationsThis lecture covers the topic of stochastic differential equations, linking probablity theory with ordinary and partial differential equations. Instructor: Choongbum Lee |

Lecture 22Play Video |
Unavailable |

Lecture 23Play Video |
Quanto Credit HedgingThis is a guest lecture on quanto credit hedging, including using mathematical models in trading. Instructor: Stefan Andreev |

Lecture 24Play Video |
HJM Model for Interest Rates and CreditThis is a guest lecture that describes the HJM model for interest rates and credit, including hedging risk on interest and credit rate derivatives. Instructor: Denis Gorokhov |

Lecture 25Play Video |
Ross Recovery TheoremThis guest lecture features the Ross Recovery Theorem. Instructor: Peter Carr |

Lecture 26Play Video |
Introduction to Counterparty Credit RiskThis 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. Instructor: Yi Tang |