Students have an overview and understand the techniques used to simulate pseudo-random numbers and stochastic processes and can apply them.Students understand the concept of Monte Carlo simulation and can use it in applications. Furthermore, they understand the benefits of variance reduction methods, know and understand the most important of these methods and can practically apply them.Students have an insight into further concepts of stochastic simulation.

Lecture with virtual blackboardExercisesPresentation of exercises

Simulation of pseudo-random numbersSimulation of stochastic processesMonte Carlo simulationVariance reduction techniquesIf time allows: Stochastic optimization, stochastic gradient descent or other topics

Analysis 1+2Lineare Algebra 1+2Stochastik 1+2

Glassermann: Monte Carlo Methods in Financial EngineeringAsmussen, Glynn: Stochastic SimmulationMüller-Gronbach, Novak, Ritter: Monte Carlo-Algorithmen

There will be a final exam, which can be repeated three times . The exams are written exams in general; if the number of participants is low (< 3), the examination can also be held orally. The first exam will take place on 24.06.2025. There will also be compulsory exercises, which students will have to present in class.

All topics that are covered in the lecture. If additional content that students have to work on themselves is relevant to the exam, this will be made clear in the lecture.

The grade results from the number of points achieved.The total number of points is 100 points.The exercises count for 15 points and the presentation of exercises for 5 points. The final exam is worth 80 points.The point scheme is as follows:[100 , 87.5] P. -> 1(87.5 , 75] P. -> 2(75 , 62.5] P. -> 3(62.5 , 50] P. -> 4(50 , 0] P. -> 5Cancellation of participation without grading is possible until 31.03.2025 via e-mail to Verena Schwarz (verena.schwarz@aau.at).