Probability and interactions

Probability courses in SMA

Contact person: Professor Juhan Aru

Bachelor (3rd semester):

Bachelor (5th and 6th semesters):

Master:

Description :

All students take the 3rd semester course “Probabilités” during the 3rd semester.

Among the optional courses, the course “Probability theory” is a core course, which can be taken already in the 5th semester. This is a prerequisite for studying advanced probability.

The courses “Processus stochastiques appliquées” and “Martingales et Applications” build on the 3rd semester course “Probabilités” and introduce important concepts related to the evolution of random phenomena over time. The first course emphasizes Markov chains and is particularly useful for students interested in statistics and Monte-Carlo methods. The second one studies discrete-time martingales and Brownian motion. Both courses prepare for further study of stochastic processes at the Master level, such as “Lattice Models”, “Théorie du calcul stochastique” and “Martingales in Financial Mathematics”.

The course “Théorie du calcul stochastique” is a first rigorous introduction to stochastic calculus for mathematics students. It has “Probability theory” as a prerequisite, though this course can be taken concurrently. It is a prerequisite for “Martingales in Financial Mathematics” and “Contrôle stochastique”.

“Martingales in Financial Mathematics” applies martingale methods and stochastic calculus in the context of mathematical finance. It has “Théorie du calcul stochastique” as a prerequisite. This course aims at introducing mathematics students to the main mathematical ideas that are used in modern financial mathematics. Students who would like to develop a significant background in financial mathematics should also consider taking statistics courses such as “Time Series” or “Quantitative Risk Management”, as well as courses in Financial Engineering, such as “Fixed income analysis”, “Financial econometrics” or “Advanced derivatives”.

The next three courses are taught from time to time:

“Contrôle stochastique” is a first course in stochastic optimization and stochastic control in discrete and continuous time. It has “Théorie du calcul stochastique” as a prerequisite.

“Lattice models” studies important discrete-time random processes, such as random walks and percolation.

“Random graphs” studies properties of large graphs that are constructed using random mechanisms.

Some other Math courses related to probability:

All the courses in statistics are related to probability.

The course “Numerical integration of stochastic differential equations” studies numerical methods for approximating stochastic processes. It has “Probabilités” and Numerical Analysis as prerequisites.

The course “Computational finance” presents numerical methods used in financial applications. Some background in stochastic processes and stochastic calculus are prerequisites.

The course “Probabilistic method” explores the use of randomness in discrete mathematics. It has “Probabilités” as a prerequisite.

Related Minors :