Stochastic differential equations and probabilistic numerical methods
Goals
This course deals with modelisation using time continous processes. The goal is to present both theoritical and pratical aspects on stochastic differentiale equations. The second part deals with numerical method to simulate stochastic 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)
Programme
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Brownian motion; Ito integral, diffusion processes, SDE. - Monte Carlo Method, important sampling, variance reduction
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Simulation de processus aléatoires ((Markov Chain and Euler Scheme) -
MCMC, Metropolis Hasting and Gibbs, Simulated annealing, stochastic gradient
Sustainable development
DD&RS level 1
Activity contextualised through environmentally sustainable development and social responsibility and/or supported by examples, exercises, applications.
Programme elements related to sustainable development goals
Monte-Carlo method, Stochastic differential equations, MCMC algorithm
Assessment method
Final mark =100% Knowledge Knowledge=max ( 100% final exam, 25% continuous assessement+75% final examen)
Bibliography
- Francis Comets et Thierry Meyre. ., Calcul stochastique et modèles de diffusions., Série Mathématiques pour le Master/SMAI, Dunod, 2006
- Nicole El Karoui et Emmanuel Gobet., Les outils stochastiques des marchés financiers, Editions de l’Ecole Polytechnique, 2011
- Bernard Bercu et Djalil Chafaï, Modélisation stochastique et simulation, Série Mathématiques pour le Master/SMAI, Dunod, 2007
Code
Responsibles
- Elisabeth MIRONESCU
- Alexandre SAIDI
- Céline HARTWEG-HELBERT