# 105.053 AKVFM stochastic control theory 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"});}); 2024W 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W 2012W 2011W 2010W 2009W 2008W 2007W 2006W 2005W 2004W

2023W, VU, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VU Lecture and Exercise
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to

• explain and apply basic facts from stochastic analysis such as Ito Integral, Ito Formula and stochastic differential equations,
• apply the dynamic programming principle,
• proof the Hamilton-Jacobi-Bellman equation and verfication theorems,
• prove the existence of the local time of the Brownian movement and to solve singular control problems,
• solve problems from financial and insurance mathematics such as optimal investments,
• minimize ruin probabilities,
• apply the martingale method in stochastic optimization and
• motivate Viscosity Solutions.

## Subject of course

a short revision of the elements of stochastic analysis as e.g. Ito Integral, Ito's formula and stochastic differential equations; dynamic programming principle, Hamilton-Jacobi-Bellman equation; verification theorems; local time of Brownian motion and singular control theory; examples from actuarial and financial mathematics as e.g. optimal investment problems, minimizing ruin probabilities, etc.; martingal methods in stochastic optimization; introduction into the theory of viscosity solutions

## Teaching methods

presentation about the theoretical foundations of the mentioned chapters. Moreover, presentations by the students.

Immanent

## Course dates

DayTimeDateLocationDescription
Mon08:00 - 11:0002.10.2023 - 22.01.2024Sem.R. DA grün 06A Beginn: 8:30
AKVFM stochastic control theory - Single appointments
DayDateTimeLocationDescription
Mon02.10.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon09.10.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon16.10.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon23.10.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon30.10.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon06.11.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon13.11.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon20.11.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon27.11.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon04.12.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon11.12.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon18.12.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon08.01.202408:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon15.01.202408:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon22.01.202408:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30

## Examination modalities

oral exam and talk

## Course registration

Begin End Deregistration end
03.09.2023 00:00 30.10.2023 23:59 04.11.2023 23:59

## Literature

No lecture notes are available.

## Language

if required in English