# 105.167 Large Deviations with Applications in Actuarial and Financial Mathematics This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2021S 2018S 2015S 2010W

2021S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Distance Learning

## Learning outcomes

After successful completion of the course, students are able to...

• explain the basic theory of large deviations (LD)
• explain some important LD results, including the main ideas of the proofs
• apply these results to problems from mathematical finance

## Subject of course

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.

## Teaching methods

lecture and discussions with students

## Mode of examination

Oral

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.

## Course dates

DayTimeDateLocationDescription
Mon10:00 - 11:0008.03.2021 Zoom (see TUWEL) (LIVE)Vorbesprechung
Fri12:00 - 13:3012.03.2021 - 18.06.2021 Zoom / siehe TUWEL (LIVE).
Large Deviations with Applications in Actuarial and Financial Mathematics - Single appointments
DayDateTimeLocationDescription
Mon08.03.202110:00 - 11:00 Zoom (see TUWEL)Vorbesprechung
Fri12.03.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri19.03.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri26.03.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri16.04.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri23.04.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri30.04.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri07.05.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri21.05.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri28.05.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri04.06.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri11.06.202112:00 - 13:30 Zoom / siehe TUWEL.
Fri18.06.202112:00 - 13:30 Zoom / siehe TUWEL.

## Examination modalities

oral exam, if necessary via Zoom

## Course registration

Begin End Deregistration end
01.02.2021 00:00 30.06.2021 23:59 31.03.2021 23:59

## Literature

No lecture notes are available.

## Language

if required in English