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18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

The lecture discusses martingales and their powerful applications in solving problems in stochastic processes, including random walks, stopping times, and gambler’s ruin probabilities, highlighting how martingale properties simplify complex analyses. It then introduces Markov processes and chains, explaining their memoryless property and applications in finance such as credit rating transitions and stock price modeling, before transitioning to regression analysis, focusing on multiple linear regression, model assumptions, and estimation techniques.

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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
assignment Activity Assignments
group_work Projects
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