Sumários
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.
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.
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.
Exercises
21 Abril 2017, 09:00 • João Guerra
Exercises about stochastic differential equations.
Discussion of several exercises about stochastic differential equations.
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.