# 105.091 AKFVM Stochastic analysis in financial and actuarial mathematics 2 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 2020S 2019S 2018S 2017S 2016S 2015S 2014S 2013S 2012S 2011S 2010S 2009S 2008S 2007S

2013S, VO, 2.0h, 4.0EC

## Properties

• Semester hours: 2.0
• Credits: 4.0
• Type: VO Lecture

## Aim of course

Stochastic analysis as needed for continuous-time financial and actuarial mathematics.

## Subject of course

Martingale representation, Gronwall's inequality, examples and solution methods for stochastic differential equations, existence and uniqueness theorem, Yamada-Watanabe condition, weak and strong solutions, Bayes' formula, Lévy's characterization of Brownian motion, several versions of Girsanov's theorem, exponential martingales, Kazamaki's criterion, Novikov's condition, Doob-Meyer decomposition, Itô diffusions, Markov property, strong Markov property, generator of an Itô diffusion, Dynkin's formula, applications

## Course dates

DayTimeDateLocationDescription
Thu09:30 - 11:1507.03.2013Sem.R. DA grün 06A Erster Termin, Beginn 9:30
Thu09:15 - 11:1514.03.2013 - 27.06.2013Sem.R. DA grün 06A .
Wed14:30 - 16:0010.04.2013Sem.R. DA grün 06A VO zum UE-Termin
Wed14:30 - 16:0017.04.2013Sem.R. DA grün 06A VO zum UE-Termin
Wed14:30 - 16:0008.05.2013Sem.R. DA grün 06A VO zum UE-Termin
Wed14:30 - 16:0029.05.2013Sem.R. DA grün 06A VO zum UE-Termin
AKFVM Stochastic analysis in financial and actuarial mathematics 2 - Single appointments
DayDateTimeLocationDescription
Thu07.03.201309:30 - 11:15Sem.R. DA grün 06A Erster Termin, Beginn 9:30
Thu14.03.201309:15 - 11:15Sem.R. DA grün 06A Weitere Donnerstags-Termine ab 9:15
Wed10.04.201314:30 - 16:00Sem.R. DA grün 06A VO zum UE-Termin
Thu11.04.201309:15 - 11:15Sem.R. DA grün 06A .
Wed17.04.201314:30 - 16:00Sem.R. DA grün 06A VO zum UE-Termin
Thu25.04.201309:15 - 11:15Sem.R. DA grün 06A .
Wed08.05.201314:30 - 16:00Sem.R. DA grün 06A VO zum UE-Termin
Thu16.05.201309:15 - 11:15Sem.R. DA grün 06A .
Thu23.05.201309:15 - 11:15Sem.R. DA grün 06A .
Wed29.05.201314:30 - 16:00Sem.R. DA grün 06A VO zum UE-Termin
Thu06.06.201309:15 - 11:15Sem.R. DA grün 06A .
Thu20.06.201309:15 - 11:15Sem.R. DA grün 06A .
Thu27.06.201309:15 - 11:15Sem.R. DA grün 06A .

oral exam

## Course registration

Begin End Deregistration end
01.06.2013 00:00 31.10.2013 23:59 30.11.2013 23:59

## Literature

Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications. 6. Edition, Springer-Verlag, 2007, ISBN 978-3-54004-758-2.

Olav Kallenberg: Foundations of Modern Probability. 2. Edition, Springer-Verlag, 2002, ISBN 0-387-953113-2.
Daniel Revuz and Marc Yor: Continuous Martingales and Brownian Motion, 3. Edition, Springer-Verlag, 1999, ISBN 3-540-64325-7.
Ioannis Karatzas und Steven E. Shreve: Brownian Motion and Stochastic Calculus. 2. Edition, Springer-Verlag, ISBN 0-38797-655-8.

Foundations:
David Williams: Probability with Martingales. Cambridge University Press, 1991, ISBN 0-521-40605-6.
Heinz Bauer: Maß- und Integrationstheorie. 2. Edition, De Gruyter, 1992, ISBN 3-11013-626-0.
Heinz Bauer: Wahrscheinlichkeitstheorie. 5. Edition, De Gruyter, 2002, ISBN 3-11017-236-4.

German