# Research Seminars

## Non-asymptotic analysis – general approach

Speaker(s):
Vladimir V. Ulyanov (Lomonosov Moscow State University)
Date:
Wednesday, July 13, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

First we give short review on recent approximation results for non-linear forms in independent random elements including asymptotic expansions. The errors of approximations could be described either in asymptotic way as an order of a remainder term with respect to number $n$ of random elements or in non-asymptotic form as a bound for remainder term with explicitly written dependence on $n$, moment characteristics and dimension $p$ of random elements or observations .

## Additional information and pricing-hedging duality in robust framework

Speaker(s):
Anna Aksamit (University of Oxford)
Date:
Thursday, July 7, 2016 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In robust approach, instead of choosing one model, one considers superhedging simultaneously under a family of models, or pathwise on the set of feasible trajectories. Usually in the literature the focus is on the natural filtration $\mathbb F$ of the price process. Here we extend that to a general filtration $\mathbb G$ including the natural filtration of the price process $\mathbb F\subset \mathbb G$. Two filtrations can model asymmetry of information on the market.

## Nonparametric statistical tests using kernels

Speaker(s):
Arthur Gretton (UCL)
Date:
Wednesday, July 6, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

I will describe a kernel approach to hypothesis testing, based on a representation of probability distributions in a reproducing kernel Hilbert space. I will first derive a metric as the distance between these representations. Next, I will describe both tests of homogeneity (of whether two samples are from the same distribution), and of independence (of whether a joint distribution factorises into a product of marginals).

## CANCELLED: Stochastic optimization and high-dimensional sampling

Speaker(s):
Eric Moulines (Ecole Polytechnique, France)
Date:
Wednesday, June 29, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Recently, the problem of designing MCMC samplers adapted to high-dimensional Bayesian inference with sensible theoretical guarantees has received a lot of interest. The applications are numerous, including large-scale inference in machine learning, Bayesian nonparametrics, Bayesian inverse problem, aggregation of experts among others.

## Stochastic Control Methods for Optimal Government Debt Management

Speaker(s):
Abel Cadenillas (University of Alberta)
Date:
Thursday, June 23, 2016 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

Motivated by the debt crisis in the world, we apply methods of stochastic control to study two problems related to government debt management. In the first problem, we consider a government that wants to control its debt ratio. The debt generates a cost for the country. The government can reduce its debt ratio, but there is a cost associated with this reduction. We apply the theory of stochastic singular control to obtain an explicit formula for the optimal government debt ceiling.

## Continuous-state Branching Processes in Random Environment

Speaker(s):
Wei Xu (Beijing Normal University)
Date:
Thursday, June 23, 2016 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

Motivated by the study of negative jumps in finance/biology, we introduce a general continuous-state branching process in random environment (CBRE-process) defined as the strong solution of a stochastic integral equation. The environment is determined by a Levy process with jumps no less than $-1$. We give characterizations of the quenched and annealed transition semigroups of the process in terms of a backward stochastic integral equation driven by another Levy process determined by the environment.

## Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions

Speaker(s):
Jakob Söhl (University of Cambridge)
Date:
Wednesday, June 22, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem corresponding to the `low frequency sampling' regime where $\Delta>0$ is fixed and $n \to \infty$. A general theorem is proved that gives conditions for prior distributions $\Pi$ on the diffusion coefficient $\sigma$ and the drift function $b$ that ensure minimax optimal contraction rates of the posterior distribution over H\"older-Sobolev smoothness classes.

## Stochastic control for a class of nonlinear kernels and applications

Speaker(s):
Chao Zhou (National University of Singapore)
Date:
Thursday, June 9, 2016 - 5:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

A stochastic control problem for a class of nonlinear stochastic kernels is studied. We prove a dynamic programming principle (DPP) for the value function by a measurable selection argument and consider several applications of the DPP including the wellposedness of second order BSDEs.
This is a joint work with Dylan POSSAMAI and Xiaolu TAN.

## Optimal investment in markets with friction

Speaker(s):
Miklos Rasonyi (Renyi Institute, Budapest)
Date:
Thursday, June 9, 2016 - 4:00pm
Location:
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We will treat optimal investment in a continuous-time market with instantaneous price impact. The novelty lies in going beyond concave utility functions and allowing non-concave preferences as well as probability distortions in the agent's objective function. This allows to treat e.g. cumulative prospect theory preferences. The main technical tool is an extension of Skorohod's representation theorem for weakly convergent sequences of probabilities.

## Slope meets Lasso: improved oracle bounds and optimality

Speaker(s):
Pierre Bellec (CREST)
Date:
Wednesday, June 8, 2016 - 10:00am
Location:
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and \ell_2 estimation rate (s/n) log(p/s) in high-dimensional linear regression on the class of s-sparse target vectors in \mathbb{R}^p. This is done under the Restricted Eigenvalue (RE) condition for the Lasso and under a slightly more constraining assumption on the design for the Slope. The main results have the form of sharp oracle inequalities accounting for the model misspecification error.