Research Seminars

Stochastic invariance of closed sets with non-Lipschitz coefficients (and applications in finance)

Speaker(s): 
Bruno Bouchard (CEREMADE - Université Paris)
Date: 
Thursday, February 2, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

This talk provides a new characterization of the stochastic invariance of a closed subset with respect to a diffusion: we extend the well known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable (on the boundary). In particular, our result can be directly applied to construct affine diffusions and polynomial preserving diffusions on any arbitrary closed set.

Laguerre basis for inverse problems related to nonnegative random variables

Speaker(s): 
Fabienne Comte (Université Paris Descartes)
Date: 
Wednesday, February 1, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will present, through two main examples, the specific properties of the Laguerre basis and show that it is a very convenient tool to solve estimation problems on R+. The first example is the regression-convolution model: an estimator of the unknown underlying function is built in two steps (deconvolution step, regression step) which are explained and discussed. Then, a risk study is conducted, that shows as usual that a bias-variance tradeoff must be performed. A model selection device is shown to solve this question.

Family-Wise separation rates for multiple testing

Speaker(s): 
Magalie Fromont-Renoir (Université Rennes)
Date: 
Wednesday, January 25, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

This joint work with Matthieu Lerasle (Univ. Paris-Saclay, France) and Patricia Reynaud-Bouret (Univ. Cote d'Azur, France) is devoted to the question of the theoretical evaluation of multiple testing procedures.Where as many first kind error-related evaluation criteria have been defined, as generalizations or relaxations of the historical Family-Wise Error Rate (FWER), very few second kind error-related criteria have been proposed in the multiple testing literature.

Bootstrap Confidence Sets for Spectral Projectors of Sample Covariance

Speaker(s): 
Alexey Naumov (Skoltech, Moscow)
Date: 
Wednesday, January 18, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Let X_1, ... ,X_n be i.i.d. sample in R^p with zero mean and the covariance matrix S. The problem of recovering the projector onto the eigenspace of S from these observations naturally arises in many applications. Recent technique from [Koltchinskii and Lounici, 2015b] helps to study the asymptotic distribution of the distance in the Frobenius norm between the true projector P_r on the subspace of the r th eigenvalue and its empirical counterpart \hat{P}_r in terms of the effective trace of S.

Model-free Ito integration via pathwise super-hedging

Speaker(s): 
David Prömel (ETH Zürich)
Date: 
Thursday, January 12, 2017 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Using Vovk’s hedging based approach to mathematical finance, one can determine sample path properties of "typical price paths" belonging to the space of continuous functions or of non-negative càdlàg functions. Interestingly, all results for "typical price paths" hold quasi surely under all martingale measures. We prove that "typical price paths" possess quadratic variation and local limes. This allows us to develop model-free Itô integration as well as pathwise stochastic calculus for local times. This talk is based on joint works with R.M. Lochowski and N. Perkowski.

Estimating latent asset-pricing factors

Speaker(s): 
Markus Pelger (Stanford University)
Date: 
Wednesday, January 11, 2017 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. Our estimator searches for factors with a high Sharpe-ratio that can explain both the expected return and covariance structure.

Adaptive weights clustering

Speaker(s): 
Vladimir Spokoiny (WIAS Berlin)
Date: 
Wednesday, December 7, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In this talk we discuss a new method of unsupervised learning for high dimensional data based on the idea of adaptive weights from Polzehl and Spokoiny (2000). The procedure recovers the unknown clustering structure without any prior information about the number of clusters, their size, distance between clusters, etc. The approach extends the popular k-mean and density based clustering procedures by using dynamically updated local weights. Theoretical results describe two major features of the method: propagation within a homogeneous region and separation between two different regions.

Risikocontrolling in der Versicherungswirtschaft - Die Solvency II Standardformel, Lineare Algebra und Diversifikation

Speaker(s): 
Joachim Paulusch (R+V Lebensversicherung AG, Risikocontrolling, Wiesbaden)
Date: 
Thursday, December 1, 2016 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Seit 01.01.2016 gilt das Aufsichtsregime Solvency II für alle Versicherungsunternehmen in Europa. Die Versicherungsunternehmen müssen eine sogenannte Solvenzkapitalanforderung berechnen und nachweisen, dass sie über Eigenmittel mindestens in Höhe der Solvenzkapitalanforderung verfügen. Dafür verwenden die meisten Versicherungsunternehmen die sogenannte Solvency II Standardformel. Wir untersuchen die Aggregation von Risiken in der Standardformel und beantworten die Fragen:

· Wie kann man Risikokapital in der Standardformel reallokieren, also fair auf Teilrisiken verteilen?

Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Speaker(s): 
Sergio Pulido (LaMME, ENSIIE, Université d'Evry Val d'Essonne)
Date: 
Thursday, December 1, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analyticexpansions for small risk aversion coefficients of the dealer. We briefly discuss related results that naturally arise when studying the replication and optimal investment problems under this model of price impact.

Estimation of linear and nonlinear functionals in nonparametric boundary models

Speaker(s): 
Gwennaëlle Mabon und Markus Reiß (HU Berlin)
Date: 
Wednesday, November 30, 2016 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point R processes we consider first the problem of efficient estimation for linear functionals of the form \int f(x)w(x)dx with unknown f and known w. We propose a simple blockwise estimator and then build up a nonparametric maximum-likelihood approach. Both methods allow for estimation with optimal rate n^{-(\beta+1/2)/(\beta+1) under \beta-Hölder smoothness or monotonicity constraints (analogue of \beta = 1).

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