Itô calculus

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Related lectures (31)

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Stochastic Calculus: Interest Rate Models

Provides an overview of stochastic calculus and its applications in interest rate models and financial modeling.

Quadratic Variation: Martingales and Stochastic Integrals

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

Stochastic Calculus: Foundations and Applications

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

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Martingale Convergence Theorem

Explains the martingale convergence theorem and its applications in probability theory.

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

Ito Lemma Variants

Explores the Ito Lemma and its variants, discussing localization and proof techniques.

Demonstration of Uniqueness Theorem

Presents a detailed proof of the uniqueness theorem for functions f and g.

Derivative of Integral with Parameter Dependency

Explores the derivative of an integral with parameter dependency and its continuity.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Girsanov: Martingales and Brownian Motion

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

Variational Calculus: Quasicovexity

Explores quasicovexity in variational calculus, discussing necessary conditions and implications on functional optimization.

Martingales and Stochastic Integration

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

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Integral Calculus: Introduction and Summary

Provides an overview of integral calculus, including Darboux sums, closed box subdivisions, and integrability of continuous functions.

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