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Martingales and Monte-Carlo Methods

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts) :
- conditional expectation, information filtering, the main properties of
martingales and their applications in modelling.
- Basics of simulation of random variables, Monte-Carlo methods, Markov
Chain Monte-Carlo (MCMC) Methods, Stochastic Algorithms (Robbins-Monro,
Simulated annealing)
The student will be able to:
· Compute a conditional expectation and to use its main properties, understand
the different types of probabilistic convergences, to show that a random process is
a martingale, to use decomposition, stopping, control and convergence theorems for
martingales.
· Simulate a random variable by different methods, use probabilistic
algorithms for solving numerical problems (computing expectations, searching for
extrema), choose appropriate techniques for variance reduction and error estimation.

Needed prerequisite


Probability and Statistics
Further lectures in probability

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...