TrainingsMasterEconomicsCoursesMathematics for finance

Master EconomicsUE Mathematics for finance

Content

Objectives :

Introducing elementary tools to analyse discrete and continuous-time random processes.

Roadmap :

1. Markov chains

1.1. Introductory Example : random walks

1.2. Markov chains on a finite state space

1.3. Markov chains on countable state spaces

1.3.1. States classification

1.3.2. Asymptotic results

2. Markovian processes in continuous time

2.1. Poisson processes

2.2. Continuous-time Markov processes

2.3. Queueing theory

3. Discrete-time random processes

3.1. Conditional expectation

3.2. Martingales

3.3. Stopping time

3.4. Convergence theorems

3.5. Applications

4. Introduction to continuous-time stochastic processes : Brownian motion

Professional skills

  • Being able to model simple situations with random processes
  • Analysing asymptotic behavior of simple random processes

Languages used

Main languages used by this course:

  • Français
  • Anglais

Bibliography

  • Stochastic Processes, S.R.S. Varadhan, AMS 2007 vol 16
  • Promenade aléatoire, Chaines de Markov et simulations ; martingales et stratégies, M. Benaïm,N. El Karoui, Ed de l’école polytechnique

Fundamental prerequisites

Basic notions in probability theory.

Structure and organisation

  • Lectures 24h
  • Exam mid-term + final exam

Volume of teachings

  • Lectures: 24 hours