Understanding the theoretical basis needed for the construction of stochastic integrals and for the study of stochastic differential equations (martingales in continuous time, stochastic integrals, Itô's formula)Knowledge on stochastic differential equations (strong and weak solutions, existence and uniqueness of solutions)Ability to solve a given stochastic differential equation (explicit solutions, numerical methods)

Each exercise class starts with a small quiz. This quiz addresses the contents covered in the last class. The exercise in the quiz will refer to the exercises on the preceding sheet. It will, however, be shorter and easier.After that, the students work on the current exercise sheet. This time should be used to discuss open problems and questions regarding the exercises. Hence, the students are expected to be familiar with the exercises and have begun working on them. The exercise sheet will not be solvable within the time of class! To assist the students, the lecturer will provide tips and additional information.  Solutions to the exercises will be available online via moodle a few days later. The students are expected to correct their exercises using the solutions on their own.The first lesson on October 05, 2023, will be used to discuss the format of the exercise class and to complete a few simple exercises together. There won’t be a quiz and there is no need for preparation!

Theoretical basis:Martingales in continuous timeStochastic integralsItô's formulaStochastic differential equations:Strong and weak solutionsExistence and uniqueness of solutionsExplicit solutionsNumerical methods

Stochastics 2Stochastic processes

Bernt Oksendal: Stochastic Differential Equations, Springer, 2010.

A total of 100 points can be reached in this course. 40 points are awarded for quizzes, and 60 points are awarded for class participation.There will be a total of 10 quizzes (beginning on October 12, 2023). They each count five points. Only the 8 quizzes with the highest number of points are taken into account at the end.Starting from October 12, 2023, the participation will be evaluated weekly according to the following scheme:0 points: The student is absent or does not participate.2.5 points: The student barely participates.5 points:  The student participates.7.5 points: The student participates actively.Only the 8 participations with the highest number of points are taken into account.Only the top 8 quizzes and top 8 participations are taken into account at the end.The marks are calculated as follows:[87.5 , 100] P. -> 1[75 , 87.5) P. -> 2[62.5 , 75) P. -> 3[50 , 62.5) P. -> 4[0 , 50) P. -> 5

Everything that is covered in the lecture and hence also in the exercise class.If additional reading is required for the lecture this will be clearly announced in the lecture.

The mark depends on the number of points the student achieves in the exercise class.Sign-out without grading is possible until October 31, 2023 by sending an e-mail to verena.schwarz@aau.at.