Stochastic Calculus: Lecture 1Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.
Doob's Decomposition TheoremCovers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.
Asset Pricing: Fundamental TheoremsCovers the fundamental theorems of asset pricing, including EMM, self-financing strategies, risk-neutral pricing, and completeness of markets.
Martingale ConvergenceExplores martingale convergence, discussing the conditions for convergence and variance in martingales.
Doob's MartingaleCovers the concept of Doob's martingale and its properties, including integrability and convergence theorem.