Girsanov Theorem - simplest version

3 Maio 2017, 09:00 • João Guerra

Pedagogical inquiry.  

Discussion of the list of assessment problems.  

Changew of measures and equivalent measures. 

The Girsanov theorem - simplest version for normal random variables.

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Exercises on diffusions, infinitesimal generators and Feynman-Kac formulas

28 Abril 2017, 09:00 • João Guerra

Exercises on diffusions, their infinitesimal generators and Feynman-Kac formulas relating PDE's and diffusions. 

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Diffusion processes as Markov processes and Feynman-Kac formula

26 Abril 2017, 09:00 • João Guerra

The Markov property for diffusion processes.

Examples.

The relationship between PDE's and SDE's.

The Infinitesimal generator of a diffusion process.

The Itô formula and the inifinitesimal generator of an Itô process.

The Feynman-Kac formula or "stochastic representation formula" for a solution of a parabolic PDE with terminal Boundary-condition.

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Exercises

21 Abril 2017, 09:00 • João Guerra

Exercises about stochastic differential equations.

Discussion of several exercises about stochastic differential equations.

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Linear SDE's. Numerical approximations.

19 Abril 2017, 09:00 • João Guerra

Example: the Black-Scholes model with Stochastic volatility.

Linear SDE's.  How to solve them. 

Existence and uniqueness theorem with n=1.

Example: the CIR  model for interest rates. 

Numerical approximations of the solutions of SDE's: the Euler scheme and the Millstein scheme. 

 

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