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Ph.D. course "The mathematics of energy markets" - Lecture 5

Ito processes and Ito-Doeblin formula. Stochastic differential equations. Back to real options in energy markets: an irreversible installation example with market impact, solved with singular…

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Lecture 57: Levy's characterization

Stochastic integral of complex-valued processes. Levy's characterization of a multidimensional Brownian motion.

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Lecture 45b: stochastic differential of a product

Stochastic differential of a product.

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Lecture 45: consequences of the Ito-Doeblin formula

A note on the integrability in the Ito-Doeblin formula. The two-dimensional case.

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Lecture 44: multidimensional Ito-Doeblin formula

The multidimensional Ito-Doeblin formula

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Lecture 22: Links between SDEs and PDEs

The Kolmogorov backward equation.

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Lecture 18: examples

The Wiener integral. Area under a Brownian motion path.

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Lecture 16: the Ito-Doeblin formula

Stochastic integral with respect to an Ito process. The Ito-Doeblin formula. Quadratic variation of an Ito process.

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