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18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

This final lecture provides an in-depth discussion of Itô’s formula and its generalizations, illustrating how it applies to functions of Brownian motion, especially in finance for modeling derivative pricing and geometric Brownian motion. It also explains the derivation of the Black-Scholes differential equation through risk-neutral hedging, the solution of the heat (diffusion) equation as a fundamental tool for solving such PDEs, and introduces more advanced stochastic differential equations like the Ornstein-Uhlenbeck process, emphasizing their broad applications beyond finance.

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## Course Info

##### Instructors

- Dr. Peter Kempthorne
- Dr. Vasily Strela
- Dr. Jake Xia

##### Departments

- Mathematics

##### As Taught In

Fall 2024

##### Level

Undergraduate

##### Topics

- Business
  - Finance
- Mathematics
  - Applied Mathematics
  - Probability and Statistics

##### Learning Resource Types

notes Lecture Notes
theaters Lecture Videos
assignment Problem Sets
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group_work Projects
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