Probability Colloquium

Critical percolation in some random fractal gaskets

Speaker(s): 
Wendelin Werner (ETH Zürich)
Date: 
Wednesday, April 23, 2014 - 5:00pm
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We will survey some recent work and work in progress with Jason Miller and Scott Sheeld on coupling between various conformal loop ensembles (these are natural random collection of loops in a two-dimensional domain). One motivation for this work is to try to shed some light on what continuous critical percolation within random CLE gaskets (the space left inbetween the loops) could be, and on the continuous analogue of the coupling between Potts models and their random cluster representations.

Minicourse on some new aspects of Backward Stochastic Differential Equations: theory and application to Finance

Speaker(s): 
Anthony Reveillac (Université Paris Dauphine)
Date: 
Tuesday, April 22, 2014 - 3:00pm to Friday, April 25, 2014 - 4:00pm
Location: 
HU Berlin, WIAS Berlin, TU Berlin

The main goal of this course is to provide an introduction to the theory of Backward Stochastic Di fferential Equations (BSDEs) and to its strong connection to Finance. We will survey the classical existence/uniqueness results for this equations together with some proofs making the course accessible to anyone who is not familiar with the theory of BSDEs, and we will present the link between BSDEs and several problems in Finance, like for instance the utility maximization problem, superheding and quantitle hedging problems.

Regularization by noise for dispersive equation

Speaker(s): 
Khalil Chouk (TU Berlin)
Date: 
Wednesday, April 16, 2014 - 6:00pm
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We discuss local and global existence for dispersive equation with irregular modulated dispersion and we show in some case that the irregularity of the modulation improve the theory of the well-posedness.

Arbitrage of the first kind and Filtration Enlargements in Semimartingale Financial Models

Speaker(s): 
Beatrice Acciaio (LSE)
Date: 
Wednesday, April 16, 2014 - 5:00pm
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will discuss the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition, in a general semimartingale financial model, under initial and under progressive filtration enlargements. In both cases, I will provide a simple and general condition which is sufficient to ensure this stability for any fixed semimartingale model. Furthermore, I will give a characterization of the NA1 stability for all semimartingale models. (This talk is based on a joint work with C. Fontana and K. Kardaras.)

Distribution-based Risk Measures and Their Implementation

Speaker(s): 
Stefan Weber (Leibniz Universität Hannover)
Date: 
Wednesday, February 12, 2014 - 6:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

Banks and insurance companies typically use distribution-based risk measures for the evaluation of their downside risks. The statistical and numerical properties of these functionals are thus important. Recently, some authors emphasized the significance of the elicitability of risk measures, a notion closely related to Huber's M-estimators. The talk characterizes elicitable distribution-based risk measures and explains their relationship to stochastic approximation theory.

Local risk-minimization for Levy markets

Speaker(s): 
Takuji Arai (Keio University)
Date: 
Wednesday, February 12, 2014 - 5:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

Locally risk-minimizing, a well-known hedging method for contingent claims in a quadratic way, is discussed by using Malliavin calculus, and some examples are introduced. We consider a financial market composed of one riskless asset and one risky asset. The risky asset price process is given by a solution to an SDE driven by a Levy process. By using a Clark-Ocone type formula under change of measure, we represents locally risk-minimizing with Malliavin derivatives of the claim to hedge.

Preference for Diversification: Different but Intricate Dimensions of Uncertainty Aversion

Speaker(s): 
Samuel Drapeau (TU Berlin)
Date: 
Wednesday, January 29, 2014 - 6:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

We study the preferences of agents for diversification and better outcomes when they are facing both, in Frank Knight's formulation, measurable as well as unmeasurable uncertainty. Following Anscombe and Aumann, such a situation can be modeled by preferences expressed on stochastic kernels, that is scenario dependent lotteries.

Planar Yang-Mills measure with high-dimensional structure group

Speaker(s): 
Antoine Dahlqvist (TU Berlin)
Date: 
Wednesday, January 29, 2014 - 5:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

We shall discuss about a random model, defined by Ambar N. Sengupta and Thierry Lévy, that is inspired by quantum field theory, giving a rigourous probabilistic interpretation of the 2D Euclidean Yang-Mills measure. For a fixed compact Lie group, called the structure group, this model gives a natural random way to associate a group element to any loop of the plane of finite length. We will describe how it can be built out of a brownian motion on the structure group and give some of its properties when the dimension of the latter goes to infinity.

A New Approach to Assess Model Risk in High Dimensions

Speaker(s): 
Carole Bernard (University of Waterloo, Canada)
Date: 
Wednesday, January 15, 2014 - 6:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

A central problem in quantitative risk management concerns the evaluation of the riskiness of a portfolio of risks ( sum of d dependent risks). This problem is mainly a numerical issue once the joint distribution of (X1,X2, . . . ,Xd) is completely specified. Unfortunately, while the marginal distributions of the risks Xi are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any computed risk measure of S is subject to model error.

Levy processes under Sublinear Expectation Spaces

Speaker(s): 
Alexandros Saplaouras (HU Berlin)
Date: 
Wednesday, January 15, 2014 - 5:00pm
Location: 
TU Berlin, Raum MA 041, Straße des 17. Juni 136, 10623 Berlin

In many applications we have to deal with the problem of model uncertainty. A relatively new tool to handle that kind of problems is G-Brownian Motion, introduced and developed by S. Peng. G-Brownian Motion is a stochastic process defined on a Sublinear Expectation Space, whose basic properties resemble to that of (classical) Brownian Motion and under which it is possible to develop Stochastic Calculus in that general framework. After that, Hu and Peng proceeded to the definition of Levy Processes under Sublinear Expectation Spaces (G-Levy processes) [1].

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