105.672 AKFVM Poisson Point Processes
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2017W, VO, 2.0h, 3.0EC

Properties

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

Aim of course

An applied lecture with integrated exercises which introduces in some of the most recent topics in Financial and Actuarial mathematics. It is based on recent and original research carried out at FAM.

Subject of course

  • Economic introduction: flash crashes, their origin and relevance; high frequency trading.
  • Mathematical introduction: Euler's product formula, Riemann's zeta function. Ideas from Riemann's habilitation thesis: analytical continuation via Jacobi's theta transformation formula; explicit formula for prime numbers via zeroes of the zeta function in the critical strip.
  • Compound Poisson process: definition, applications in actuarial mathematics and geometry.
  • Levy processes: an introduction via Poisson point processes.
  • Brownian excursions: a PPP on a function space.
  • Limit order book:  PPP meet number theory. Laplace-Mellin transform of a flash crash distribution via Riemann's Xi function.
  • Stochastic partial differential equations: solution via time reverted local time; discussion of Hölder continuity via this example.

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Wed14:00 - 15:4511.10.2017 - 24.01.2018Sem.R. DA grün 04 .
AKFVM Poisson Point Processes - Single appointments
DayDateTimeLocationDescription
Wed11.10.201714:00 - 15:45Sem.R. DA grün 04 .
Wed18.10.201714:00 - 15:45Sem.R. DA grün 04 .
Wed25.10.201714:00 - 15:45Sem.R. DA grün 04 .
Wed08.11.201714:00 - 15:45Sem.R. DA grün 04 .
Wed22.11.201714:00 - 15:45Sem.R. DA grün 04 .
Wed29.11.201714:00 - 15:45Sem.R. DA grün 04 .
Wed06.12.201714:00 - 15:45Sem.R. DA grün 04 .
Wed13.12.201714:00 - 15:45Sem.R. DA grün 04 .
Wed20.12.201714:00 - 15:45Sem.R. DA grün 04 .
Wed10.01.201814:00 - 15:45Sem.R. DA grün 04 .
Wed17.01.201814:00 - 15:45Sem.R. DA grün 04 .
Wed24.01.201814:00 - 15:45Sem.R. DA grün 04 .

Course registration

Not necessary

Curricula

Literature

No lecture notes are available.

Language

if required in English