Stochastik mit Finanzmathematik

Vorträge des Schwerpunkts Stochastik

Studierende und Gäste sind herzlich eingeladen!

Auf dieser Seite finden Sie Informationen über Vorträge folgender Seminare:

  • Rhein-Main Kolloquium Stochastik (Gemeinsames Kolloquium der Arbeitsgruppen Stochastik TU Darmstadt / Gutenberg-Universität Mainz / Goethe-Universität Frankfurt)
  • Stochastisches Kolloquium (Forschungsseminar des Schwerpunkts Stochastik)
  • Oberseminar Stochastik (Forschungsseminar für Doktoranden und Masterstudenten)
  • Verweis auf weitere interessante Vorträge (außerhalb des Frankfurter Schwerpunkts Stochastik)

Vorträge in chronologischer Rheinfolge:


Oberseminar Stochastik:

Mittwoch, 18. Dezember 2019, Raum 711 gr

14:00 Uhr: Vortrag von Maurice Georgi

Stochastische Modellierung von segmentweisen linearen Plastidbewegungen

Rhein-Main-Kolloquium Stochastik:

Freitag, 06.12.2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Simone Warzel (TU München): Quantum spin glasses: a mathematical challenge

The theory of classical mean-field spin glasses is a well-established and celebrated field within probability theory. The addition of a constant perpendicular magnetic field introduces a non-commuting term into the energy of such spin glasses and hence causes quantum effects. The main aim of this talk is to give an overview over some of the motivations for the study of quantum spin glasses. I will also review some first mathematical results in this field. Among them is a derivation of the key features of the thermal phase diagram of the simplest of all mean-field spin glasses, the quantum random energy model.

16.15-16.45 Uhr Kaffeepause

16.15 Uhr Matthias Erbar (Bonn): A variational characterization of the Sine_ß point process

The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_ß process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine_ß process. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional. Joint work with Martin Huesmann and Thomas Leblé 

MathFinanceColloquium/ Berufspraxiskolloquium:

Donnerstag, 05.12.2019, 16:15 Uhr, Raum 711 groß

Dr. Jürgen Bierbaum (Alte Leipziger Versicherung): Bewertung in unvollständigen Märkten - Finanzmathematik in der Lebensversicherung

Die Mehrzahl der Lebensversicherungsverträge in Deutschland enthält langfristige Zinsgarantien. Die Preisfindung sowie die ökonomische und bilanzielle Bewertung dieser Verträge erfordert die Entwicklung komplexer finanz- und versicherungsmathematischer Modelle. Wegen der Illiquidität der Märkte für langfristige Kapitalanlagen ist auch die Kalibrierung der Bewertungsmodelle eine nichttriviale Aufgabe. Zusätzlich sollte bereits beim Produktdesign auf eine kapitaleffiziente Struktur der Verpflichtungen geachtet werden. Im Vortrag werden einige wichtige Aufgabenstellungen aus der Praxis sowie gängige Ansätze zu ihrer Lösung vorgestellt.

Im Anschluss ist eine kurze Nachsitzung im Frankfurt and Friends geplant.


Montag, 18. November um 12:30 Uhr in Raum 110

Sprecher: Prof. Dr. Dirk Metzler, FB Biologie, LMU München

Hybridzone zwischen Rabenkrähen und Nebelkrähen: Artbildung allein durch Paarungspräferenzen?

Aaskrähen gibt es in zwei Farbmorphen: in Westeuropa als schwarze Rabenkrähen und in Nord-, Ost-, und Südeuropa als grau-schwarz-gemusterte Nebelkrähen. Wo die Verbreitungsgebiete der beiden Farbmorphen an einader grenzen,z.B. in Deutschland an der Elbe, kommt es zur Hybridisierung. Die Krähen scheinen jedoch Verpaarung innerhalb ihrer jeweiligen Farbmorphe zu bevorzugen. Mittels mathematischer Modellierung und numerischen Simulationen untersuchen wir, ob solche assortativen Paarungspräferenzen eine stabile Koexistenz der beiden Farbmorphen erklären kann und eventuell zur Aufspaltung der Aaskrähen in zwei Arten führen wird. Wir passen unser Modell an populationsgenetische Daten an und berücksichtigen die genetische Architektur der Gefiederfärbung. Eine überraschende Vorhersage unserer Modellierung ist, dass die Hybridzone einer räumlichen Dynamik unterliegt, die stark davon abhängt, wie zwei Genloci für die Ausprägung der Gefiederfärbung interagieren. (Kooperation mit Jochen Wolf, Joshua Penalba und Ulrich Knief)

Oberseminar Stochastik:

Mittwoch, 13. November 2019, Raum 711 gr

14:00 Uhr: Vortrag von Prof. Dr. John T Whelan (School of Mathematical Sciences (Statistics), Rochester Institute of Technology and Institute for Theoretical Physics)

Bayesian Applications of the Bradley-Terry Model to Sports Team Ratings

The Bradley-Terry-Zermelo model has been widely used to evaluate paired comparison experiments, with applications ranging from taste tests to rating chess players. In this model, each object being compared has a strength parameter, and the probability of winning a comparison is proportional to this strength. I consider the application of this model to the problem of rating or ranking teams based on their game results when the schedule is not balanced. While the traditional maximum-likelihood implementation is adequate when there are many games played, the results can be undesirable over short seasons. E.g., if a team wins all of its games, the MLE of its strength is infinite. This can be resolved with a Bayesian approach where a joint posterior probability distribution is deduced for the Bradley-Terry strengths. Such an application requires a choice of prior distribution for these strengths. While most authors have considered families of prior distributions which can reflect the experimenters' additional knowledge about the objects, for the application as a rating system, the different teams should be judged on equal terms. I will discuss some possible choices of prior distribution suitable for this application, as well as hierarchical models which leverage families of prior distributions, with examples from sports such as baseball, American football, and ice hockey.

Stochastisches Kolloquium:

Mittwoch, 30. Oktober 2019, 14:15 Uhr in Raum 903:

Hsien-Kuei Hwang (Academia Sinica, Taipei)

Stirling numbers of the second kind: the history of early developments and an elementary approach to asymptotic normality

A historical account is given of the early developments of the Stirling numbers of the second kind: in contrast to those in the West, those in the East, notably in Japan, have remained mostly unknown with the corresponding combinatorial origin traced back to at least 1600.
I will talk about the background, the mathematical developments in Japan in the Edo Period (1603--1868), and the corresponding developments in the West. Then after a brief survey on the various methods for proving the asymptotic normality N(n/log n, n/(log n)^2) of the Stirling numbers of the second kind, I will introduce a very simple, elementary approach to proving the local and central limit theorems. The approach, based on the principle of inclusion and exclusion and Stirling's formula for the factorial, is also applicable to several dozens of other examples in the literature and in the OEIS (Online Encyclopedia of Integer Sequences). This talk is based on joint works with Xiaoling Dou (Waseda University) and with Chong-Yi Li (Academia Sinica).

Oberseminar Stochastik:

Mittwoch, 16. Oktober 2019, Raum 711 gr

14:00 Uhr: Master-Abschlussvortrag Lucas Then

Cumulant-Covariances and their Application within Homogeneous Marked Poisson Process Models for Parallel Spike Trains


Montag, 02.09.2019, 17:15 Uhr, Raum 711 groß

Jiling Cao (Auckland University of Technology):
Inferring information from the S&P 500 and CBOE indices: The more the merrier ?

The Chicago Board Options Exchange (CBOE) updated the CBOE Volatility Index (VIX) in 2003 and further launched the CBOE Skew Index (SKEW) in 2011, in order to measure the 30-day risk-neutral volatility and skewness of the S&P 500 Index (SPX). In this work, we mainly compares the information extracted from the SPX and CBOE indices in terms of the SPX option pricing performance. Based on our analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while, the SKEW is very noisy and does not contain much important information for option prices.

Oberseminar Stochastik:

Mittwoch, 14. August 2019, Raum 711 gr

14:00 Uhr: Bachelor-Abschlussvortrag von Anna-Lena Weinel

Minima und Maxima einer verzweigenden Irrfahrt

15:00 Uhr: Bachelor-Abschlussvortrag von Jan Lukas Igelbrink 

Rekursive Baumprozesse: Endogenität und bivariate Eindeutigkeit

Rhein-Main Kolloquium Stochastik:

Freitag, 24. Mai 2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15:15 Roland Bauerschmidt (University of Cambridge): 

Dynamics of strongly correlated spin systems
I will discuss some results on the problem of understanding the long-time behaviour of Glauber and Kawasaki dynamics of spin systems in the regimes of strong correlations. This is joint work with Thierry Bodineau.

16:15 – 16:45 Uhr:    Kaffee und Tee

16:45 h Prof. Dr. Chiranjib Mukherjee (Universität Münster):

Gaussian multiplicative chaos in the Wiener space
In the classical finite dimensional setting, a Gaussian multiplicative chaos (GMC) is obtained by tilting an ambient measure by the exponential of a centred Gaussian field indexed by a domain in the Euclidean space. In the two-dimensional setting and when the underlying field is "log-correlated", GMC measures share close connection to the 2D Liouville quantum gravity, which has seen a lot of revived interest in the recent years.
A natural question is to construct a GMC in the infinite dimensional setting, where techniques based on log-correlated fields in finite dimensions are no longer available. In the present context, we consider a GMC on the classical Wiener space, driven by a (mollified) Gaussian space-time white noise. In $d\geq 3$, in a previous work with A. Shamov and O. Zeitouni, we showed that the total mass of this GMC, which is directly connected to the (smoothened) Kardar-Parisi-Zhang equation in $d\geq 3$, converges for small noise intensity to a well-defined strictly positive random variable, while for larger intensity (i.e. for small temperature) it collapses to zero. We will report on joint work with Yannic Bröker (Münster) where we study the endpoint distribution of a Brownian path under the GMC measure and show that, for low temperature, the endpoint GMC distribution localizes in few spatial islands and produces asymptotically purely atomic states.

Stochastisches Kolloquium:

Mittwoch, 8. Mai 2019, 14:15 Uhr in Raum 711 gr:

Christian Webb (Aalto/Finland)

An introduction to log-correlated fields and multiplicative chaos

Log-correlated fields are stochastic processes arising e.g. in various models of statistical mechanics, probabilistic combinatorics, and probabilistic number theory. They are characterized by having a logarithmic singularity in their covariance. Multiplicative chaos measures are random fractal measures built from these log-correlated fields. I will briefly discuss the precise definition of these objects, how multiplicative chaos measures can be used to study extreme values of log-correlated fields, and time permitting, how this type of results can be applied e.g. in random matrix theory.