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AG Stochastik (Wintersemester 2018/19)

Seminar: Dienstag 15:45-17:15 SR 2.59
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
Seminarleitung Prof. Dr. Günter Last
Sprechstunde: nach Vereinbarung.
Zimmer 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30)
Email: guenter.last@kit.edu

Studierende und Gäste sind jederzeit herzlich willkommen. Wenn nicht explizit anders unten angegeben, finden alle Vorträge im Seminarraum 2.59 im Mathebau (Gebäude 20.30) statt.

Dienstag, 29.01.2019

15:45 Uhr Charl Pretorius (The North West University, Südafrika)

Bootstrap confidence bounds: splitting the sample for higher-order accuracy

Abstract: We propose a new method, based on sample splitting, for constructing bootstrap confidence bounds for a parameter appearing in the regular smooth function model. It has been demonstrated in the literature that the well-known percentile-t bootstrap confidence bounds are typically second-order accurate. Using our version of the bootstrap percentile-t method, confidence bounds of third- and even fourth-order accuracy can be obtained. Furthermore, whereas the standard percentile bounds are typically first-order accurate, the new bounds achieve second-order accuracy. In the case where the parameter of interest is the population mean, we derive for each confidence bound the exact coefficient of the leading term in an asymptotic expansion of the coverage error, although similar results may be obtained for other parameters such as the variance, the correlation coefficient, and the ratio of two means. We show that fourth-order accurate equal-tailed confidence intervals may be obtained from the newly proposed bounds, as opposed to the typical first-order accuracy of the standard intervals. It is also shown that the good properties of the new percentile-t bound carry over to regression problems. A small simulation study illustrates the behaviour of the confidence bounds for small to moderate sample sizes.
(JWH Swanepoel)

Dienstag, 22.01.2019

15:45 Uhr M. Sc. Franz Nestmann (KIT, Institut für Stochastik)

Zentrale Grenzwertsätze im Random Connection Model

Dienstag, 08.01.2019

15:45 Uhr M. Sc. Bernard Effah Nyarko (African Institute for Mathematical Sciences, Ghana und Brandenburgische Technische Universität Cottbus - Senftenberg)

Optimal Insurance/Investment Problems under Stochastic Volatility and Model Uncertainty

Abstract: In this talk, problems of optimal excess-of-loss and investment policies for an ambiguity averse insurer who is concerned with the misspecification errors and uncertainty around the physical model. The insurer can invest in a risk-free and risky asset whose price process follows a stochastic volatility model. This problem can be seen as a robust optimal control for the insurer and by the method of dynamic programming, opti-mal strategies are obtained for an exponential type utility. Numerical sensitivity analyses are performed
for the model parameters on the optimal policies and its economic implication.

Dienstag, 18.12.2018

15:45 Uhr Olivier Menoukeu Pamen (African Institute for Mathematical Sciences, Ghana und University Liverpool)

Strong rate of convergence for the Euler-Maruyama approximation of SDEs with singular drift coefficients

Dienstag, 04.12.2018

15:45 Uhr M.Sc. Daniel Schmithals (Institut für Stochastik, KIT)

Model-independent finance via martingale optimal transport

Abstract: We motivate the concept of model-independent finance and explain the basic idea. We adapt the theory of classical optimal transport in order to introduce the problems of martingale optimal transport which have interpretations in terms of pricing and hedging of derivatives. We deduce a strong duality result for the two problems in a general setting showing that the solutions of the problems correspond to best-possible derivative price bounds and associated hedging strategies. Finally, we improve the price bounds using information on return covariances.

Dienstag, 27.11.2018

15:45 Uhr Dr. Daniel Gaigall (Leibniz Universität Hannover)

Über eine asymptotische relative Effizienz basierend auf den erwarteten Volumina von Konfidenzbereichen

Abstract: Wir diskutieren eine asymptotische relative Effizienz für Konfidenzbereiche eines mehrdimensionalen Pa-rameters basierend auf den erwarteten Volumina der Konfidenzbereiche. Unter Standardannahmen erge-ben sich die asymptotischen relativen Effizienzen über bestimmte Potenzen der Quotienten der Grenzwer-te der erwarteten Volumina. Diese Grenzwerte werden für Konfidenzbereiche korrespondierend mit be-stimmten Plug-in-Schätzern, Likelihood-Quotienten-Tests und Wald-Tests explizit hergeleitet. Unter Regula-ritätsbedingungen ist die asymptotische relative Effizienz für jedes dieser Verfahren bezüglich eines jeden anderen dieser Verfahren gleich 1. Die Resultate werden angewendet auf mehrdimensionale Normalvertei-lungen und Multinomialverteilungen in einem recht allgemeinen Setting.
(L. Baringhaus und D. Gaigall)

Dienstag, 13.11.2018

15:45 Uhr Dr. Peter Hieber (Universität Ulm)

Constrained non-concave utility maximization: An application to life insurance contracts with guarantees

Abstract: We study a problem of non-concave utility maximization under a fair pricing constraint. The framework finds many applications in, for example, the optimal design of managerial compensation or equity-linked life insur-ance contracts. Deriving closed-form solutions, we observe that the fair pricing constraint will reduce the riskiness of the optimal strategies substantially. In an extensive numerical section, we analyze innovative retirement products that adapt the investment strategy of the premium pool according to the policyholder’s preferences, modeled as constant relative risk aversion (CRRA). Such products are a response to the loss of attractiveness of traditional life insurance contracts with guarantees that are negatively affected by increasing solvency requirements for return guarantees and a general decrease in interest rate levels. Taking into ac-count that retirement products are usually tax-privileged, we find that fairly priced guarantee contracts that follow this optimal investment strategy lead to a higher expected utility level than asset investments.
(joint with An Chen, Thai Nguyen)

Dienstag, 30.10.2018

15:45 Uhr Prof. Dr. Günter Last (KIT, Institut für Stochastik)

Hyperuniform stable matchings of point processes