Kolmogorov Equations

29 Abril 2016, 14:00 • João Guerra

Kolmogorov backward and forward equations (or Fokker-Planck equation) . Example. 

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Girsanov theorem

26 Abril 2016, 14:00 • João Guerra

Kolmogorov Backward partial differential equation and stochastic representation formula for the solution.

Stopping times: basic properties.

Change of probability measures and densities. Equivalent probability measures.

The Girsanov Theorem (simple version). Proof.

The general Girsanov Theorem.

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Feynman-Kac formulas

22 Abril 2016, 14:00 • João Guerra

Feynman-Kac formulas - examples and exercises.

The inifinitesimal generator of a diffusion and the Kolmogov "backward" partial differential equation.

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The Diffusions as Markov processes and Feynman-Kac formula

19 Abril 2016, 14:00 • João Guerra

The diffusions are Markov processes.

Transition probabilities for Diffusions.  Example.

The infinitesimal generator of a diffusion.

Parabolic PDE's with terminal condition and the Feynman-Kac formula (stochastic representation formula). The Heat equation. Example.

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Stochastic differential equations

15 Abril 2016, 14:00 • João Guerra

Existence and uniqueness theorem for one-dimensional stochastic differential equations. Example. The CIR (Cox-Ingersoll-Ross) stochastic differential equation.

How to solve linear stochastic differential equations.

Numerical methods for stochastic differential equations: the Euler scheme and the Millstein scheme.

 

 

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