After successful completion of the course, students are able to...
The theory of large deviations deals with "rare" events, whose probability decreases exponentially w.r.t. some parameter. A classical example are sample means which are "far" from the true expectation inspite of a "large" sample size. We will cover the following subjects from the general theory: Cramer's theorem, Gärtner-Ellis theorem, general LDP (large deviation principle), Varadhan's lemma, and fundamentals of the Freidlin-Ventzell theory about sample path large deviations. Applications: Option pricing by Monte Carlo (importance sampling), large losses in credit risk management, asymptotics of option prices for short maturities.I will try to adjust the proportion of theory vs. financial applications to the background and interests of the participants.
lecture and discussions with students
Necessary technical equipment: Device with internet access, microphone, camera. *One* device is sufficient, but feel free to use two devices for the exam. In any case, during the exam you have to be able to write something and show it to me, be it digitally or by paper + camera.
oral exam, if necessary via Zoom
