# 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_21",{id:"j_id_21",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_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2024S 2021S 2018S 2015S 2010W

2015S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture

## Aim of course

Understanding the fundamentals of a classical area of probability theory, including applications in risk management and option pricing.

## 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.

## Course dates

DayTimeDateLocationDescription
Mon14:00 - 16:0002.03.2015 - 09.03.2015Sem.R. DA grün 06A .
Mon12:30 - 14:0016.03.2015 - 29.06.2015Sem.R. DC rot 07 .
Large Deviations with Applications in Actuarial and Financial Mathematics - Single appointments
DayDateTimeLocationDescription
Mon02.03.201514:00 - 16:00Sem.R. DA grün 06A .
Mon09.03.201514:00 - 16:00Sem.R. DA grün 06A .
Mon16.03.201512:30 - 14:00Sem.R. DC rot 07 .
Mon23.03.201512:30 - 14:00Sem.R. DC rot 07 .
Mon20.04.201512:30 - 14:00Sem.R. DC rot 07 .
Mon27.04.201512:30 - 14:00Sem.R. DC rot 07 .
Mon04.05.201512:30 - 14:00Sem.R. DC rot 07 .
Mon11.05.201512:30 - 14:00Sem.R. DC rot 07 .
Mon18.05.201512:30 - 14:00Sem.R. DC rot 07 .
Mon08.06.201512:30 - 14:00Sem.R. DC rot 07 .
Mon15.06.201512:30 - 14:00Sem.R. DC rot 07 .
Mon22.06.201512:30 - 14:00Sem.R. DC rot 07 .
Mon29.06.201512:30 - 14:00Sem.R. DC rot 07 .

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
066 415 Actuarial Mathematics Not specified
860 Technical Mathematics Not specified
860 GW Optional Courses - Technical Mathematics Not specified

## Literature

No lecture notes are available.

German