Stochastic Calculus: Interest Rate Models

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Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Explores martingales, Brownian motion, and measure transformations in probability theory.

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Covers the fundamental theorems of asset pricing, including EMM, self-financing strategies, risk-neutral pricing, and completeness of markets.

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Covers martingales, stochastic integration, and localizing processes using stopping times.

Explores the foundation of stochastic calculus, emphasizing deterministic and memoryless processes.

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Explores arbitrage in multiperiod models, covering dynamic trading, absence of arbitrage, trading strategies, discounted prices, and martingales.