Research Group "Stochastic Algorithms and Nonparametric Statistics"

Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Winter Semester 2021/2022

09.11.2021 Simon Breneis (Wias Berlin)
Markovian approximations of stochastic Volterra equations with the fractional kernel (online talk)
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low Hölder-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in $N$. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.
16.11.2021 n.n.

23.11.2021 n.n.

30.11.2021 Long-Hao Xu (University of Manchester)
Limiting behavior of the gap between the largest two representative points of statistical distributions (online talk)
The problem of selecting a given number of representative points retaining as much information as possible arises in many situations. It can also be considered as a problem of approximating a continuous distribution by a discrete distribution. In this talk, we are interested in these points reaching the minimum value of mean squared error (we call these points MSE RPs). We illustrate the relationship between MSE RPs and doubly truncated mean residual life (DMRL) as well as mean residual life (MRL), and we discuss the limiting behavior of the gap between the largest two MSE RPs. In simulation studies, we assess the statistical performance of MSE RPs for various distributions in terms of moment estimation and resampling technique. We also discuss the relationship between the tail of the distribution and the gap of MSE RPs.
07.12.2021 Oleg Butkovsky (WIAS Berlin)
Inverting the Markovian projection: A reproducing kernel Hilbert space approach (online talk)
14.12.2021 Uli Sauerland, Anton Benz (Leibniz-Zentrum Allgemeine Sprachwissenschaft)
Numerical challenges in linguistic pragmatics
11.01.2022 Pavel Dvurechensky (WIAS Berlin)
Hessian barrier algorithms for non-convex conic optimization (online talk)
We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced in [Bomze, Mertikopoulos, Schachinger, and Staudigl, Hessian barrier algorithms for linearly constrained optimization problems, SIAM Journal on Optimization, 2019]. Our approach is based on a potential-reduction mechanism and attains a suitably defined class of approximate first- or second-order KKT points with the optimal worst-case iteration complexity O(ε^-2) (first-order) and O(ε^-3/2) (second-order), respectively. A key feature of our methodology is the use of self-concordant barrier functions to construct strictly feasible iterates via a disciplined decomposition approach and without sacrificing on the iteration complexity of the method. To the best of our knowledge, this work is the first which achieves these worst-case complexity bounds under such weak conditions for general conic constrained optimization problems. Based on the joint work with Mathias Staudigl.
18.01.2022 Yangwen Sun (HU Berlin)
High dimensional change-point detection: A complete graph approach (online talk)


last reviewed: December 6, 2021 by Christine Schneider