Objectives
This course deals with modelisation using time continous processes. The goal is to present both theoritical and pratical aspects on Markov processes. It is more specifically for students of Mathematic, Actuarial and quantitative finance options and Masters. It is requiered to have followed a course on theory of probability (for example the course in S8 in Ecole Centrale de Lyon)
Palabras clave
Brownian Motion, Martingales, Ito calculus, Numerical simulations, Monte Carlo Markov chain methods
Programme
- Probability theory (Reminders)
- Stochastic processes, Brownian Motion
- Martingales
- Stochastic integral
- Stochastic differential equations
- Diffusion approximation
- (BE) Methods of Monte Carlo Markov Chains and sampling
Learning Outcomes
- Modelisation with time-continous Markov processes
- Ito calculus
- Approximation of a diffusion. Practical aspects
- Gibbs algorithme or annealing method; Practical aspects
Assesment
Final mark =60% Knowledge + 40% Know-how Knowledge= 100% final exam Know-how= 100% continuous assessment
Specific concerning Master students