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AG Stochastik (Sommersemester 2018)

Seminar: Dienstag 15:45-17:15 SR 2.58
Seminarleitung Prof. Dr. Günter Last
Sprechstunde: nach Vereinbarung.
Zimmer 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30)
Email: guenter.last@kit.edu
Seminarleitung Prof. Dr. Nicole Bäuerle
Sprechstunde: nach Vereinbarung.
Zimmer 2.016 Kollegiengebäude Mathematik (20.30)
Email: nicole.baeuerle@kit.edu
Seminarleitung Prof. Dr. Vicky Fasen-Hartmann
Sprechstunde: Nach Vereinbarung.
Zimmer 2.053 Kollegiengebäude Mathematik (20.30)
Email: vicky.fasen@kit.edu
Seminarleitung Prof. i. R. Dr. Norbert Henze
Sprechstunde: nach Vereinbarung
Zimmer 2.020, Sekretariat 2.002 Kollegiengebäude Mathematik (20.30)
Email: henze@kit.edu
Seminarleitung Prof. Dr. Daniel Hug
Sprechstunde: Nach Vereinbarung.
Zimmer 2.051 Kollegiengebäude Mathematik (20.30)
Email: daniel.hug@kit.edu

Studierende und Gäste sind jederzeit herzlich willkommen. Wenn nicht explizit anders unten angegeben, finden alle Vorträge im Seminarraum 2.58 im Mathebau (Gebäude 20.30) statt.

Dienstag, 17.07.2018

15:45 Uhr Prof. Bikram Das (Singapore University of Technology and Design)

Heavy tails in a robust news vendor model

Abstract: A solution to the newsvendor problem with ambiguity in the demand distribution was provided by Scarf (1958). The optimal order quantity in this problem is computed for the worst possible distribution from a set of demand distributions that is characterized by partial information, such as moments. A simple observation indicates that the optimal order quantity when only the rst two moments of the distribution are known, the model is also optimal for a censored Student-t distribution with innite variance. In this talk, we generalize this "heavy-tail optimality" property of the distributionally robust newsvendor model to the case when information on the first and the n-th moment is known for any n > 1 (not necessarily an integer). Unlike the mean-variance setting, this problem does not appear to be solvable in a simple closed form. We show that for high critical values, the optimal order quantity for the distributionally robust newsvendor is also optimal for a regu-larly varying distribution with parameter indexed by n.
(This is a joint work with Karthik Natarajan and Anulekha Dhara).

Dienstag, 10.07.2018

15:45 Uhr Prof. Dr. Markus Riedle (King's College London)

Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes

Abstract: In this talk we consider the stochastic Cauchy problem driven by a cylindrical Lévy process. Here, a cylindrical Lévy process is understood in the classical framework of
cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or Gaussian space-time white
The first part of the talk is devoted to introduce cylindrical Lévy processes and their characteristics and to present some examples. We develop a stochastic integration theory for deterministic, operator-valued integrands with respect to cylindrical Lévy processes and to provide necessary and sufficient conditions for a function to be integrable. In the second part, we apply the developed theory to show that the Ornstein-Uhlenbeck process is the weak solution of the stochastic Cauchy problem. For this purpose, we have to derive a stochastic version of Fubini's result without requiring any condition on the moments. The talk finishes with discussing some path regularities of the Ornstein- Uhlenbeck process and presenting some open problems.
Some parts of this talks are based on a joint work with Umesh Kumar.

Dienstag, 05.06.2018

15:45 Uhr Dr. Ferenc Fodor (University of Szeged, Hungary)

On the Lp dual version of the Minkowski problem

Abstract: We will mainly discuss the solution of the existence part of the Lp version of the qth dual Minkowski problem
for p > 1 and q > 0. The Lp dual Minkowski problem, formulated by Lutwak, Yang and Zhang, provides a unification of
several other variants of the question. We will concentrate on the more geometric parts of the argument and especially
on the discrete case. We will also describe the regularity properties of the solution with the help of the corresponding
Monge-Amp`ere equation. This is joint work with K´ aroly J. B¨ or ¨oczky (R´enyi Insitute, Budapest, Hungary).

Dienstag, 29.05.2018

15:45 Uhr M.Sc. Dennis Müller (Institut für Stochastik, KIT)

Central Limit Theorems for Geometric Functionals of Gaussian Excursion Sets

Dienstag, 08.05.2018

15:45 Uhr M. Sc. Julian Sester (Universität Freiburg)

Extensions of the Optimal Martingale Transport Problem

Abstract: We investigate the optimal transport problem with martingale constraints and its application to model-independent price bounds for financial derivatives when including information about the variance of returns on the underlying security. This additional information can be extracted from prices of certain exotic deriva-tives traded on OTC markets. Our theoretical results comprise a dual version of the modified transport prob-lem. The numerical results indicate that tighter price bounds can be obtained when taking into account such additional information on the variance of returns. In this respect, our results have important implications for the practical applicability and relevance of model-independent price bounds. Moreover, we discuss a modified transport problem which arises when assuming the underlying process to be Markovian and investigate the effects on the dual problem and on model-independent price bounds.