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2022W, 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 - 11:0003.10.2022 - 23.01.2023Sem.R. DA grün 06A Beginn: 8:30
Mon08:30 - 11:0019.12.2022 (LIVE)(Nur) Online via Zoom - siehe TUWEL-Kurs
AKVFM stochastic control theory - Single appointments
DayDateTimeLocationDescription
Mon03.10.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon17.10.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30 - ONLINE VIA ZOOM: https://tuwien.zoom.us/j/96584873499?pwd=M0d2VFYwcmdOelRkU1BpVmhEVFdBZz09
Mon24.10.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon31.10.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon07.11.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon14.11.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon21.11.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon28.11.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon05.12.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon12.12.202208:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon19.12.202208:30 - 11:00 (Nur) Online via Zoom - siehe TUWEL-Kurs
Mon09.01.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon16.01.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30
Mon23.01.202308:00 - 11:00Sem.R. DA grün 06A Beginn: 8:30

## Examination modalities

oral exam and talk

## Course registration

Begin End Deregistration end
04.09.2022 00:00 31.10.2022 23:59 05.11.2022 23:59

## Literature

No lecture notes are available.

## Language

if required in English