Prof. Dr. Christian Bender
Prof. Dr. Henryk Zähle
Stochastics Research Seminar
Thursdays 14-16 in room 217 (SR 6), building E2 4, or as announcedTalks in the winter semester 2015/16:
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Wednesday, 24.02.2016, 14:15:
Tommi Sottinen (University of Vaasa)
Fredholm representation for Gaussian processes with applications
Abstract:
We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. In particular, we prove an Ito formula that is, as far as we know, the most general Malliavin-type Ito formula for Gaussian processes so far. Finally, we give applications to equivalence in law and series expansions of Gaussian processes.
This is joint work with Lauri Viitasaari
Room 316 (SR 10), building E2.4
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Wednesday, 24.02.2016, 10:00:
Daniel Kreber (Saarland University)
Der Kolmogorov-Smirnov-Test
Room 217 (SR 6), building E2.4
Talks in the summer semester 2015:
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Friday, 04.09.2015, 10:15:
Laura Heine (Saarland University)
Zur Konvergenzgeschwindigkeit der Binomialbaum-Methode bei der Optionsbewertung
Abstract:
Zunächst werde ich das Black-Scholes-Modell und das Binomial-Modell kurz vorstellen und erläutern, wie mit Hilfe der Skorokhod-Einbettung die Einbettung des diskontierten Aktienkurses des Binomial-Modells in den des Black-Scholes-Modell erfolgt. In Anlehnung an das Paper von John B. Walsh „The rate of convergence oft the binomial tree scheme" werde ich anschließend den Fehler des Binomial-Modells als Approximation des Black-Scholes-Modells detailliert betrachten. Es ist möglich, den Fehler genau zu bestimmen, indem der Fehler gesplittet wird in einen Fehler, der nur von globalen Eigenschaften und einen, der nur von lokalen Eigenschaften der Auszahlungsfunktion einer Option abhängt.
Room 217 (SR 6), building E2.4
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Wednesday, 01.07.2015, 14:15:
Patrick Kern (Saarland University)
Qualitative Robustheit von Punktschätzern und Anwendung auf kollektive Versicherungsrisiken
Room 217 (SR 6), building E2.4
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Wednesday, 24.06.2015, 14:15:
Alexandra Lauer (Saarland University)
Nichtparametrische Schätzung von Risikomaßen kollektiver Risiken
Room 217 (SR 6), building E2.4
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Wednesday, 10.06.2015, 14:15:
Matthias Sroczinski (University of Konstanz)
Hilbert Space Valued Supersolutions of Stochastic Backward Differential Equations
Abstract:
For a separable real Hilbert space K we study a K-valued BSDE with terminal condition xi in L^2 and generator g(y,z). We fix an orthonormal basis on K and equip K with the partial order induced by this basis. Then we define the notion of a K-valued supersolution of the BSDE in respect to that partial order. If we assume the generator to be positive, diagonal and each of its component to be convex in z, monotone in y and jointly lower semicontinuous we can prove existence and uniqueness of a minimal supersolution.
Room 217 (SR 6), building E2.4
Talks in the winter semester 2014/15:
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Thursday, 05.03.2015, 10:15:
Stefan Schröder (Saarland University)
Bias-Reduktion mittels Bootstrap beim Schätzen von Risikomaßen
Room 217 (SR 6), building E2.4
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Thursday, 26.02.2015, 13:15:
Dr. Yana Kinderknecht (Saarland University)
Feynman formulae for evolution semigroups generated by some Markov processes
Room 217 (SR 6), building E2.4
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Wednesday, 21.01.2015, 12:15:
Dr. Ibrahim Ekren (ETH Zurich)
Viscosity solutions of path-dependent partial differential equations
Abstract:
In this talk, we define derivatives of functionals on the space of continuous paths and give an introduction to path-dependent partial differential equations (PPDEs). These equations extend the well-known Feynman-Kac Formula to a non-Markovian framework. Since the space of continuous paths is not locally compact, we cannot rely on the theory of viscosity solutions for PDEs and need to develop a new approach. We define viscosity solutions for both fully nonlinear PPDEs and for the obstacle problem. We present comparison and stability results for these equations and give the relation between PPDEs and some non-Markovian stochastic control problems. This talk is based on joint works with Nizar Touzi and Jianfeng Zhang.
Room 217 (SR 6), building E2.4
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Thursday, 30.10.2014, 15:15:
Dr. Federico Polito (University of Turin)
On the fractional Poisson process and related topics
Abstract:
We will present a generalization of the classical Poisson process in a fractional sense. Fractionality is introduced both in time and state-space by replacing the integer-order time-derivative with a fractional derivative and the difference operator acting in space with a fractional difference operator often used in time series analysis. Several results will be described by specializing the model in the time-fractional or the space-fractional case. Finally two subordination relationships involving stable subordinators and their right-inverse processes will be highlighted.
Room 203 (SR 7), building E2.4
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Wednesday, 29.10.2014, 12:15:
Dr. Angelica Pachon Pinzon (University of Turin)
On the relation between the preferential attachment, Simon and Yule models
Abstract
Room 217 (SR 6), building E2.4
Talks in the summer semester 2014:
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Thursday, 12.06.2014, 14:15:
Dr. Lauri Viitasaari (Aalto University)
On pathwise stochastic integrals with applications
Abstract:
This talk aims to present some recent developments in the theory of pathwise stochastic integration together with applications. More precisely, we study the existence and properties of integrals of form $\int_0^{T}f(X_u) dY_u$, where the function $f$ is of locally bounded variation and $X$ and $Y$ are certain H\"older continuous processes. Since the function $f$ may have discontinuities, it implies that $f(X_u)$ is of unbounded $p$-variation for every $p\geq 1$. Consequently, classical Young integration theory or rough path theory introduced by Lyons cannot be applied. As an application, we present some results related to integral representations of random variable. Such representations are motivated especially by mathematical finance, where integral representations can be viewed as hedging equations of claims.
Room 217 (SR 6), building E2.4
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Wednesday, 28.05.2014, 14:30:
Konstantin Eckle (Saarland University)
Schwache Konvergenz in nicht-separablen metrischen Räumen und empirische Prozesse
Room 217 (SR 6), building E2.4
Talks in the winter semester 2013/14:
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Wednesday, 12.02.2014, 14:15:
Dr. Joscha Diehl (TU Berlin)
Stochastic control with rough paths
Abstract:
We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We propose a formulation based on rough paths and then obtain a generalization of Rogers' duality formula [L. C. G. Rogers, 2007] from discrete to continuous time. We also make the link to old work of [Davis-Burstein, 1987].
This is joint work with Peter Friz and Paul Gassiat.
Room 319 (SR 9), building E2.4
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Wednesday, 15.01.2014, 14:45:
Dr. Christian Mönch (TU Darmstadt)
Typische Distanzen in komplexen Netzwerken
Room 319 (SR 9), building E2.4
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Wednesday, 11.12.2014, 14:15:
Justus Rübel (Saarland University)
Monotoner Grenzwertsatz für BSDEs
Room 319 (SR 9), building E2.4
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Wednesday, 27.11.2013, 14:15:
Thomas Kruse (Université d'Evry)
BSDEs with singular terminal condition and control problems with constraints
Abstract:
We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [7] and [8]. We perform a verification and discuss special cases for which the control problem has explicit solutions.
Joint work with Stefan Ankirchner and Monique Jeanblanc.
Room 319 (SR 9), building E2.4
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Wednesday, 13.11.2013, 12:00:
Matthias Thiel (Saarland University)
Mischeigenschaften von Markov-Ketten Monte Carlo Methoden für das Hochzeitsproblem
Abstract:
Ich werde zunächst das Hochzeitsproblem erläutern und den Gale-Shapley-Algorithmus zur Konstruktion von stabilen Zuordnungen vorstellen. Daraufhin werde ich die Frage klären, warum aus Fairnessüberlegungen heraus Markov-Ketten Monte Carlo (MCMC) Methoden für das Hochzeitsproblem interessant sein könnten. Anschliessend werde ich auf sogennante optimierte Listen und das Konzept der Rotationen eingehen, um eine geeignete Markov-Kette auf dem Gitter der stabilen Zuordnungen zu definieren. Schließlich werde ich Resultate von Bhatnagar, Greenberg und Randall (2008) vorstellen, die zeigen, dass die konstruierte Markov-Kette in verschiedenen Modellen des Hochzeitsproblems nur sehr langsam ins Gleichgewicht konvergiert.
Room U.11 (SR 3), building E2.5
Talks in the summer semester 2013:
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Friday, 27.09.2013, 10:30:
Dr. Leif Döring (University of Zürich)
Selbstähnliche Markovprozesse und Sprung SDEs
Abstract:
Die Darstellung selbstähnlicher Markovprozesse durch Levy Prozesse geht zurück auf Arbeiten von Lamperti in den 1970ern. In den letzten 10 Jahren wurde das Verhalten dieser Prozesse im Ursprung genauer untersucht. Wir diskutieren eine Sprung SDE Darstellung, mittels derer Fragen über das Verhalten im Ursprung auf schwache Eindeutigkeits Eigenschaften zurückgeführt werden können.
Room 316 (SR 10), building E2.4
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Thursday, 19.09.2013, 14:30:
Dr. Hasanjan Sayit (University of Durham)
Absence of arbitrage in a general framework
Abstract:
Cheridito (Finance Stoch 7:533-553, 2003) studies a financial market that consists of a money market account and a risky asset driven by a fractional Brownian motion. It is shown that arbitrage possibilities in such markets can be excluded by suitably restricting the class of allowable trading strategies. In this talk, we discuss an analogous result in a multi-asset market where the discounted risky asset prices follow more general non-semimartingale models. In our framework, investors are allowed to trade between a risk-free asset and multiple risky assets by following simple trading strategies that require a minimal deterministic waiting time between any two trading dates. We present a condition on the discounted risky asset prices that guarantee absence of arbitrage in this setting. We give examples that satisfy our condition and study its invariance under certain transformations.
Room U.16 (SR 4), building E2.5
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Thursday, 12.09.2013, 14:30:
Dr. Mikko Pakkanen (Aarhus University)
Volatility estimation for ambit fields
Abstract:
Ambit fields are multiparameter stochastic processes, defined as moving averages of volatility-modulated infinitely-divisible random measures. They have been recently applied, for example, to the modeling of turbulent velocity fields and the term structure of electricity forward prices. In my talk, I will discuss how power variations can be used to estimate the realized volatility of a two-parameter ambit field constructed using a Gaussian random measure, a white noise. In particular, I will present limit theorems for power variations of ambit fields driven by white noise under infill asymptotics.
Room U.39 (Zeichensaal), building E2.5
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Thursday, 05.09.2013, 14:30:
Arturo Valdivia (Universitat de Barcelona)
Filtered Lévy processes and applications
Abstract:
The fractional Brownian motion (fBm) can be obtained by integrating a deterministic kernel with respect to a standard Brownian motion. A 'filtered Lévy process' is a generalization of the fBm, obtained by taking different kernel as integrand and a different Lévy process as integrator. Recently, these processes have attracted a lot of attention due to both its theoretical interest and potential use in many applied fields. Consequently, a stochastic calculus with respect to these processes has been developed, obtaining so far many interesting results. In this talk we shall discuss integration with respect to filtered processes, and give expressions for functionals of these integrals. As an application, we shall present a credit risk model in order to price Convertible Contingent Bonds.
Room 319 (SR 9), building E2.4
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Thursday, 25.07.2013, 14:30:
Alexandra Lauer (Saarland University)
Numerische Berechnung des fairen Preises von Flexible Caps im LIBOR-Market Modell durch Simulation
Abstract:
Ich werde zunächst auf die Dynamik der Zinsraten im LIBOR-Market Modell eingehen und den cash-flow Prozess eines Flexible Caps definieren. Danach werde ich in Anlehnung an die Arbeiten von John Schoenmakers, Sven Balder und Antje Mahayni das Problem der Bestimmung optimaler Stoppzeiten und deren numerischer Konstruktion erläutern. Auf dieser Basis lassen sich dann untere Schranken für den Optionspreis aufstellen. Für die Konstruktion der oberen Schranken werde ich dann auf den sog. dualen Ansatz auf Grundlage der Doob-Zerlegung eingehen.
Room 319 (SR 9), building E2.4
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Dienstag, 23.07.2013, 10:30:
Bastian Groß (Universtität Trier)
Calibration of SDE-based Financial Market Models via an Adjoint Technique
Room U.16 (SR 4), building E2.5
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Donnerstag, 18.07.2013, 14:30:
Prof. Denis Belomestny (Universtität Duisburg-Essen)
Pricing American options via multi-level fast approximation methods
Abstract:
We propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level low biased estimate for the price of an American option.
Room 319 (SR 9), building E2.4
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Thursday, 04.07.2013, 14:30:
Martin Hakenesch (Saarland University)
Superhedging in endlichen Märkten
Room 319 (SR 9), building E2.4
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Thursday, 27.06.2013, 14:30:
Philip Oberacker (Saarland University)
An Itô formula for convoluted Lévy processes - The white noise-case
Room 319 (SR 9), building E2.4
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Thursday, 20.06.2013, 14:30:
Dr. Robert Knobloch (Saarland University)
An Itô formula for convoluted Lévy processes - The L^2-case
Room 319 (SR 9), building E2.4
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Thursday, 13.06.2013, 14:30:
Prof. Christian Bender (Saarland University)
A simple proof of the Wick-Itô formula for Gaussian processes
Room 319 (SR 9), building E2.4
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Thursday, 06.06.2013, 14:30:
Sarah Klein (Saarland University)
Tug-of-war model for bidirectional intracellular cargo transport
Room 319 (SR 9), building E2.4
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Wednesday, 27.03.2013:
Jia Zhuo (University of Southern California)
A probabilistic numerical method for high-dimensional fully nonlinear PDEs
Room 203 (SR 7), building E2.4
Last modified on 07 October 2014 by Philip Oberacker