Concept

Semimartingale

Related lectures (21)

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.

Stochastic Integration: First Steps

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

Stochastic Calculus: Integrals and Processes

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

Semimartingale: Joint Variation Process

Covers semimartingales, Ito's lemma, and polynomial demonstrations, emphasizing the management of second-order terms and induction reasoning.

Stochastic Calculus: Itô's Formula

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

Generalization of Martingales: Sub- & Supermartingales

Explores the generalization of martingales to sub- and supermartingales with a focus on convergence properties.

Generalizations to Sub- & Supermartingales

Covers the generalizations of sub- & supermartingales and the existence of random variables.

Doob's Martingale

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Girsanov: Martingales and Brownian Motion

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

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Martingales and Brownian Motion

Explores martingales, Brownian motion, submartingales, descents monitoring, and convergence theorems with practical examples.

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.

Martingales: Exponential Martingales

Explores martingales, particularly exponential martingales and their properties under different probability measures.

Martingale Convergence Theorems

Explores the convergence of martingales under specific conditions and previews upcoming topics on martingale theorems and inequalities.

Risk-neutral Valuation

Explores risk-neutral valuation for European derivatives, EMMs, trading strategies, and market securities in financial modeling.

Parameter Estimation of SDEs with Linear Response Theory

Explores parameter estimation of SDEs using Linear Response Theory and covers challenges, examples, algorithms, and convergence.

Dynamic Programming: Portfolio Optimization

Explores dynamic programming for optimizing portfolio choices and asset pricing theory.

Point Processes: Extremal Limit Theorems

Explores the theory of point processes and their applications to extremes, emphasizing the Laplace functional and Kallenberg's theorem.