Introduction to Martingales
arXiv:2407.11914
Abstract
This paper introduces Martingales by covering introductory measure theory concepts and the Lebesgue Integration and Conditional Expectation. It follows up with proofs of Kolomorgov's Theorem on conditional expectations, the Martingale Property, and the Pythagorean Theorem on Martingales. Finally, it ends with Martingales' applications in finance.
18 pages