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AG Stochastik (Sommersemester 2015)

Seminar: Dienstag 15:45-17:15 Z 1
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


Wenn nicht explizit anders angegeben, finden die Vorträge im SR 2.58 (Geb. 20.30) statt.

Dienstag, 14.07.2015

15.45 Uhr Anton Popp (Institut für Stochastik, KIT):

Risikosensitive Stopp-Probleme für zeitstetige Markov-Ketten

Abstract: Dieser Vortrag widmet sich der Betrachtung sogenannter risikosensitiver Stopp-Probleme. Hierbei wird ver-sucht, einen durch eine zeitstetige Markov-Kette beeinflussten Prozess optimal zu stoppen, um den daraus resultierenden risikosensitiven Nutzen des Gewinns zu maximieren. Der Begriff "risikosensitiv" bezeichnet in der Literatur traditionell die Betrachtung des obigen Problems unter Exponential-Nutzen. Hier jedoch soll der Begriff "risikosensitiv" allgemein für beliebige Nutzenfunktionen aufgefasst werden. In diesem Vortrag soll ein Lösungsansatz vorgestellt werden, der das Stopp-Problem in ein zeitdiskretes Problem transformiert und die optimale Lösung als Fixpunkt einer Integralgleichung interpretiert. Weiter werden die strukturellen Eigen-schaften optimaler Stopp-Regeln untersucht und Bedingungen gegeben, unter denen diese vom sogenann-ten One-Step-Look-Ahead-Typ sind.

Dienstag, 07.07.2015

15.45 Uhr Prof. Fabio Bellini (Universität Mailand):

Elicitable risk measures and expectiles

Abstract: The talk is divided into two parts. In the first part we will recall the notion of elicitable risk measure, discuss its financial relevance and present several characterization results; in particular, we will prove that an elicitable convex risk measure is necessarily a shortfall risk measure of generalized type, thus refining a well-known result of Weber (2006). In the se-cond part of the talk, we will focus on the expectiles, that are the only example of an elicitable and coherent risk measure. After discussing their properties, we will show by means of numerical examples that expectiles are a perfectly reasonable alternative to more established risk measures such as Value at Risk or Expected Shortfall.

Dienstag, 30.06.2015

15.45 Uhr Prof. Bikramjit Das (Singapore University of Technology and Design):

Hidden large deviations for regularly varying Lévy processes

Abstract: We discuss (hidden) large deviations of regularly varying Lévy processes. It is well-known that large deviations of such processes are related to one large jump. We exhibit that by stripping away appropriate spaces, we can see subsequent jumps of the process under proper scaling. We study convergences under the notion of M-convergence which has been used to study regular variation on a variety of cones on complete separable metric spaces. (This is a joint work with Parthanil Roy.)

Dienstag, 15.06.2015

15.45 Uhr Prof. Dr. Werner Stuetzle (University of Washington):

Nonparametric Clustering

Abstract: The goal of clustering is to detect the presence of distinct groups in a data set and assign group labels to the observations. Nonparametric clustering is based on the premise that the observations may be regarded as a sample from some underlying density in feature space and that groups correspond to modes of this density. I will present some of the basic ideas of nonparametric clustering and discuss open problems.

Dienstag, 02.06.2015

15.45 Uhr Prof. Dr. Zakhar Kabluchko (Westfälische Wilhelms-Universität Münster):

Intrinsic volumes of Sobolev ellipsoids, Gaussian processes, and random convex hulls

Abstract: A formula due to Sudakov relates the first intrinsic volume of a convex set to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first intrinsic volume of some finite and infinite-dimensional convex sets including regular polytopes, unit balls with respect to Sobolev-type norms, and ellipsoids in the Hilbert space. These results can be used to compute expected volumes of various random convex hulls, for example the convex hull of the Brownian motion.

Dienstag, 26.05.2015

15.45 Uhr Dr. Sebastian Engelke (Ecole Polytechnique Fédérale de Lausanne):

Extremes on River Networks

Abstract: Max-stable processes are suitable models for extreme events that exhibit spatial dependencies. The de-pendence measure is usually a function of Euclidean distance between two locations. In this talk, we model extreme river discharges on a river network in the upper Danube catchment, where flooding regularly causes huge damage. Dependence is more complex in this case as it goes along the river flow. For non-extreme data a Gaussian moving average model on stream networks was proposed by Ver Hoef and Peterson (2010). Inspired by their work, we introduce a max-stable process on the river network that allows flexible modeling of flood events and that enables risk assessment even at locations without a gauging station. Re-cent methods from extreme value statistics are used to fit this process to a big data set from the Danube area.

Dienstag, 12.05.2015

15.45 Uhr Prof. An Chen (Universität Ulm):

Risk-shifting and optimal asset allocation in life insurance: The impact of regulation

Abstract: In a typical participating life insurance contract, the insurance company is entitled to a share of the return surplus as compensation for the return guarantee granted to policyholders. This call-option-like stake gives the insurance company an incentive to increase the riskiness of its investments at the expense of the policy-holders. The conflict of interests can partially be solved by regulation deterring the insurance company from taking excessive risk. In a utility-based framework where default is modeled continuously by a structural ap-proach, we show that a flexible design of regulatory supervision can be beneficial for both the policyholder and the insurance company.

Dienstag, 05.05.2015

15.45 Uhr Prof. Clément Dombry (Université de Franche-Comté):

Concurrence probabilities for extremes

Abstract: The statistical modelling of spatial extremes has recently made major advances. Much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes. To address this gap, this paper introduces the notion of extremal concurrence. Suppose that one measures precipitation at several synoptic stations over multiple days. We say that extremes are concurrent if the maximum precipitation over time at each station is achieved simultaneously, e.g., on a single day. Un-der general conditions, we show that the finite sample concurrence probability converges to an asymptotic quantity, deemed extremal concurrence probability. Using Palm calculus, we establish general expressions for the extremal concurrence probability through the max-stable process emerging in the limit of the componentwise maxima of the sample. Explicit forms of the extremal concurrence probabilities are obtained for various max-stable models and several estimators are introduced. In particular, we prove that the pair-wise extremal concurrence probability for max-stable vectors is precisely equal to the Kendall’s τ. The esti-mators are evaluated by using simulations and applied to study the concurrence patterns of temperature extremes in the United States. The results demonstrate that concurrence probability can provide a powerful new perspective and tools for the analysis of the spatial structure and impact of extremes.

Dienstag, 28.04.2015

15.45 Uhr Prof. Anna Jaskiewicz (Wroclaw University of Technology):

Bequest games with unbounded utilities

Abstract: Deterministic bequest games were first discussed by Phelps and Pollak (1968) in the context of some con-siderations in the theory of economic growth. In their model, it is assumed that each generation lives, saves and consumes over just one period. Moreover, each generation cares about consumption of its immediate descendant and leaves it a bequest. This leftover part constitutes the next generation's inheritance that is determined by some continuous production function. The existence of Markov perfect equilibria in such games in the class of left continuous strategies of bounded variation was proved independently by Bernheim and Ray (1983) and Leininger (1986).
I will present a stochastic model of bequest games, in which the following generation's endowment is de-scribed by a stochastic transition probability function that is assumed to be weakly continuous. The transition probability need not be non-atomic and therefore, the deterministic case is also included in the analysis. Another feature is the fact that there are two manners considered according to which a current generation derives its utility from its own consumption and that of its descendant. The first case is a standard expected
utility, whereas the second case takes into account a risk attitude of the generation and employs the entropic risk measure. Finally, I will mention some generalisation to the purely deterministic case.

Dienstag, 21.04.2015

15.45 Uhr Michael Schrempp (KIT):

Zur Asymptotik des maximalen Abstandes zufälliger Punkte in einer ebenen Menge mit ellipsenähnlichen Rändern

Abstract: Eine wichtige Kenngröße von unabhängigen und identisch im Raum verteilten zufälligen Punkten ist der maximale Abstand. In der Vergangenheit wurde die Asymptotik dieser Kenngröße bereits für viele verschiedene zugrunde gelegte Verteilungen untersucht. Die-ser Vortrag widmet sich der Verteilungskonvergenz des maximalen Abstandes bzgl. einer bisher nicht betrachteten Klasse von Verteilungen mit einem beschränkten Träger in der Ebene. Als einfachster Spezialfall tritt dabei die Gleichverteilung innerhalb einer Ellipse auf.

Dienstag, 14.04.2015

15.45 Uhr Alexander Jordan (HITS / KIT):

Of Quantiles and Expectiles:Consistent Scoring Functions, Choquet Representations, and Forecast Rankings

Abstract: In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the directive.
We show that any scoring function that is consistent for a quantile or an expectile functional, respec-tively, can be represented as a mixture of extremal scoring functions that form a linearly parameterized fami-ly. Scoring functions for the mean value and probability forecasts of binary events constitute important ex-amples. The quantile and expectile functionals along with the respective extremal scoring functions admit appealing economic interpretations in terms of thresholds in decision making.
The Choquet type mixture representations give rise to simple checks of whether a forecast domi-nates another in the sense that it is preferable under any consistent scoring function. In empirical settings it suffices to compare the average scores for only a finite number of extremal elements. Plots of the average scores with respect to the extremal scoring functions, which we call Murphy diagrams, permit detailed com-parisons of the relative merits of competing forecasts.
This is joint work with Werner Ehm, Tilmann Gneiting and Fabian Krüger.