Search for tag: "martingale property"

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Lecture 64: stochastic volatility models duration 1 hour 9 minutes Lecture 64: stochastic volatility models Lecture 64: stochastic volatility models	Lecture 64: stochastic volatility models The martingale representation theorem and stochastic volatility models. local martingale martingale representation theorem martingale property stochastic volatility From Tiziano Vargiolu 11 plays 0
Lecture 58: the Girsanov theorem duration 33 minutes 33 seconds Lecture 58: the Girsanov theorem Lecture 58: the Girsanov theorem	Lecture 58: the Girsanov theorem The Girsanov theorem in the multidimensional case. Novikov's condition. girsanov theorem girsanov kernel equivalent probabilities brownian motion martingale property novikov condition From Tiziano Vargiolu 26 plays 0
Lecture 57: Levy's characterization duration 36 minutes 2 seconds Lecture 57: Levy's characterization Lecture 57: Levy's characterization	Lecture 57: Levy's characterization Stochastic integral of complex-valued processes. Levy's characterization of a multidimensional Brownian motion. complex-valued stochastic integral levy's characterization theorem cross variation quadratic variation martingale property brownian motion ito-doeblin formula From Tiziano Vargiolu 13 plays 0
Lecture 56: Kolmogorov backward equation and… duration 1 hour 8 minutes Lecture 56: Kolmogorov backward equation and… Lecture 56: Kolmogorov backward equation and Feynman-Kac representation	Lecture 56: Kolmogorov backward equation and Feynman-Kac representation The Kolmogorov backward equation. The Feynman-Kac representation formula in the whole space and in bounded domains. Application: barrier options. kolmogorov backward equation markov property feynman-kac representation martingale property exit time barrier options From Tiziano Vargiolu 30 plays 0
Lecture 34: multidimensional stochastic calculus duration 1 hour 22 minutes Lecture 34: multidimensional stochastic calculus Lecture 34: multidimensional stochastic calculus	Lecture 34: multidimensional stochastic calculus Multidimensional stochastic integrals: definition, linearity, mean and covariance matrix, martingale property, cross-variation. stochastic integral linearity covariance operator ito isometry martingale property cross variation From Tiziano Vargiolu 19 plays 0
Lecture 26: change of probability with a… duration 52 minutes 57 seconds Lecture 26: change of probability with a… Lecture 26: change of probability with a filtration	Lecture 26: change of probability with a filtration Equivalent probability measures. Conditional expectation and martingales under the new probability. absolutely continuous probabilities equivalent probabilities conditional expectation martingale property filtration density of probabilities density process From Tiziano Vargiolu 20 plays 0
Lecture 22: Links between SDEs and PDEs duration 27 minutes 33 seconds Lecture 22: Links between SDEs and PDEs Lecture 22: Links between SDEs and PDEs	Lecture 22: Links between SDEs and PDEs The Kolmogorov backward equation. kolmogorov backward equation martingale property parabolic equations partial differential equations ito-doeblin formula stochastic differential equations markov property From Tiziano Vargiolu 22 plays 0
Lecture 9: stochastic integral as a stochastic… duration 33 minutes 39 seconds Lecture 9: stochastic integral as a stochastic… Lecture 9: stochastic integral as a stochastic process	Lecture 9: stochastic integral as a stochastic process The stochastic integral is a continuous martingale. continuity martingale property stochastic integral From Tiziano Vargiolu 22 plays 0
Lecture 5: Brownian martingales duration 29 minutes 51 seconds Lecture 5: Brownian martingales Lecture 5: Brownian martingales	Lecture 5: Brownian martingales Examples of Brownian martingales: Brownian motion, exponential and square of a Brownian motion. brownian motion martingales martingale property exponential martingale From Tiziano Vargiolu 25 plays 0