Rohan Shah
Published 2024-07-16Version 1
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.
Pointwise defined version of conditional expectation with respect to a random variable
On the Feller-Dynkin and the Martingale Property of One-Dimensional Diffusions
Conditional Expectation as Quantile Derivative
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