Research Seminars

Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Regression

Speaker(s): 
Xiaohong Chen (Yale University)
Date: 
Wednesday, October 21, 2015 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

This talk makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h_0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h_0 and its derivatives when h_0 is approximated via a spline or wavelet sieve.

Application of PPDEs to stochastic differential games

Speaker(s): 
Ibrahim Ekren (ETH Zürich)
Date: 
Thursday, July 9, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

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 new approaches. We present new results on degenerate PPDEs and apply them to the study of non-Markovian stochastic differential games.

Robust pricing, hedging and investing in discrete time

Speaker(s): 
Ludovic Tangpi (HU Berlin)
Date: 
Thursday, July 9, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We provide a theoretical framework for pricing, hedging and investing in a model-independent financial market. Our method relies on representation results for convex increasing functionals and extends to hedging problems with given marginals. Based on joint works with P. Cheridito and M. Kupper.

Testing the Specification in Random Coefficient Models

Speaker(s): 
Christoph Breunig (Humboldt-Unverisität zu Berlin)
Date: 
Wednesday, July 8, 2015 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

In this talk, we suggest and analyze a new class of specification tests for random coefficient models. They allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function.

Partial orderings of default predictions

Speaker(s): 
Walter Krämer (Technische Fakultät Dortmund)
Date: 
Monday, July 6, 2015 - 2:00pm
Location: 
Spandauer Straße 1, Room 23

We compare and generalize various partial orderings of probability forecasters according to the quality of their predictions. It appears that the calibration requirement is quite at odds with the possibility of some such ordering. However, if the requirements of calibration and identical right marginals are relaxed, comparability obtains more easily.

Low-rank volatility estimation for high-dimensional Lévy processes and low frequency observations

Speaker(s): 
Mathias Trabs (University Paris-Dauphine)
Date: 
Wednesday, July 1, 2015 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Whenever the modelling of random processes in biology, finance or physics requires to incorporate jumps, Lévy processes are one of the building blocks under consideration. Consequently, their statistical analysis attracted much attention in the last decades. We first review some results on the nowadays well understood nonparametric estimation of the characteristic triplet of a univariate Lévy process based on low frequent observations. The underlying inverse problem is ill-posed, where the degree of ill-posedness is determined by the characteristic triplet itself.

Performance von Mutual Sector Funds

Speaker(s): 
Rainer Schulz (The University of Aberdeen)
Date: 
Monday, June 29, 2015 - 2:00pm
Location: 
Spandauer Straße 1, Room 23

Sector mutual funds have experienced high growth in the US over the past two decades. We examine the performance of the sector fund industry and the relative performance of different sectors, such as funds that invest in real estate stocks or tech stocks. We assess the performance using several different benchmarks.

Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

Speaker(s): 
Laurent Denis (University of Le Mans, Frankreich)
Date: 
Thursday, June 25, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We present an approach to absolute continuity and regularity of laws of Poisson functionals based on the framework of local Dirichlet forms. The method mainly uses the chaos decomposition of the Poisson L^2 space which extends naturally to a chaos decomposition of the domain of the candidate closed form and gives rise to a new explicit calculus : it consists in adding a particle and taking it back after computing the gradient.

Benchmarked Risk Minimization

Speaker(s): 
Eckhard Platen (University of Technology Sydney)
Date: 
Thursday, June 25, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numeraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Föllmer, Sondermann and Schweizer. The latter relies on a quadratic criterion, requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure. The proposed concept of benchmarked risk minimization avoids these restrictive assumptions.

An Adaptive Functional Autoregressive Forecasting Model to Predict Electricity Price Curves

Speaker(s): 
Ying Chen (National University Singapore)
Date: 
Wednesday, June 24, 2015 - 10:00am
Location: 
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Electricity price forecasting is becoming increasingly relevant in the competitive energy markets. We provide an approach to predict the whole electricity price curves based on the adaptive functional autoregressive (AFAR) methodology. The AFAR has time varying operators that allow it to be safely used in both stationary and non-stationary situations. Under stationarity, we develop a consistent maximum likelihood (ML) estimator with closed form, where the likelihood function is defined on the parameters' subspace or Sieves.

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