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401-3612-00L 5 Credits DR , MSC , WBZ D-ITET , D-MATH , D-INFK
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Stochastic Simulation

Lecturers & Examiners: Dr. Fabio Sigrist
VVZ CR n/a

Last Updated: 2026-02-05 16:30:06

Abstract

This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo.

Objective

Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R.

Content

Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC).

Resources

Lecture Notes

A script will be available in English.

Literature

P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition).

General Information

Language
English
Levels
DR , MSC , WBZ
Frequency
Every two years

Examination

Type
session examination
Mode
written 120 minutes
Aids
Closed book; simple pocket calculator with no communication capability.
The performance assessment is offered in the session after the course unit and once more in the subsequent exam session half a year later. Apart from this, repetition is only possible after re-enrolling.

Course Components

Type Title Time & Place Hours
lecture Stochastic Simulation
  • Tue 14:15-16:00 (ETF C 1)
2 h weekly
exercise Stochastic Simulation
  • Tue 16:15-18:00 (ETF C 1)
1 h weekly

Offered In