Research Group "Stochastic Algorithms and Nonparametric Statistics"

Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2023

18.04.2023 Wilfried Kenmoe Nzali (WIAS Berlin)
Optimal control problem in energy finance (hybrid talk)
25.04.2023 Dr. Sven Wang (Massachusetts Institute of Technology)
On polynomial-time mixing of MCMC for high-dimensional posterior distributions (online talk)
We consider the problem of generating random samples from high-dimensional posterior distributions. We will discuss both (i) conditions under which diffusion-based MCMC algorithms mix in polynomial-time (based on as well as (ii) situations in which MCMC suffers from an exponentially long mixing time (based on We will focus on the setting of non-linear inverse regression models. Our positive results on polynomial-time mixing are derived under local `gradient stability' assumptions on the forward map, which can be verified for a range of well-known non-linear inverse problems involving elliptic PDE, as well as under the assumption that a good initializer is available. Our negative results on exponentially long mixing times hold for `cold-start' MCMC. We show that there exist non-linear regression models in which the posterior distribution is unimodal, but there exists a so-called `free entropy barrier', which local Markov chains take an exponentially long time to traverse.
02.05.2023 N.N.

09.05.2023 N.N.

16.05.2023 Dr. Christian Bayer (WIAS Berlin)
An introduction to Hawkes processes (hybrid talk)
Hawkes processes are a prototypical example of self-exciting point processes. They are one of the most useful processes in science, engineering, and finance. Introduced as a model for time and magnitude of earthquakes, they have also been used as models for epidemics, crimes, traffic accidents, and so on. In finance, they are often used as models for order flow, for instance in order to solve the optimal execution problem, or to analyse market activity. We give a short introduction into Hawkes processes, including motivation, definitions and basic properties, and simulation.
23.05.2023 Prof. Dr. Daniel Walter (HU Berlin)
Nonsmooth minimization in infinite dimensional spaces meets sparse dictionary learning (hybrid talk)
We propose a novel method for problems involving nonsmooth but convex regularization terms over infinite dimensional function spaces . It resembles a dictionary learning algorithm which switches between the update of a dictionary $\mathcal{A}_k$ of extremal points of the unit ball of the regularizer and of a sparse represenation of the iterate $u_k$ in its conic hull by solving a finite dimensional~$\ell_1$-regularized problem. Imposing additional assumptions on the involved dual variables , its asymptotic linear convergence is shown. The theoretical results are accompanied by numerical experiments involving challenging regularizers such as the Benamou-Brenier energy as well as the BV-seminorm, highlighting both, the sharpeness of our results as well as the practical applicability of the method.

06.06.2023 Simon Breneis (WIAS Berlin)
American options under rough Heston (hybrid talk)
The rough Heston model is a popular option pricing model in mathematical finance. However, due to the non-semimartingale and non-Markovian characteristics of its volatility process, simulations can be prohibitively expensive in practice. Building on previous works, we approximate the volatility process with an N-dimensional diffusion, yielding a Markovian approximation of the rough Heston model. Then, we introduce a weak discretization scheme to simulate paths of these Markovian approximations. Our numerical experiments show that these approximations converge at a second-order rate as the number of time steps approaches infinity. We leverage these approximations to price American options under the rough Heston model.






last reviewed: May 16, 2023 by Christine Schneider