From the 1 of 7 linked papers with an AI index.
7 papers
Universality and Approximation Rates of Graph Neural Networks with Random Features
Lukas Gonon, Thilo Meyer-Brandis, Niklas Weber
The paper proves that message‑passing graph neural networks with partially random node features can universally approximate any permutation‑invariant or equivariant function on fix…
On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models
Alexander Kalinin, Thilo Meyer-Brandis, Annika Steibel
We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-…
Computing Systemic Risk Measures with Graph Neural Networks
Lukas Gonon, Thilo Meyer-Brandis, Niklas Weber
This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from B…
Regularity of Solutions of Mean-Field -SDEs
Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis
We study regularity properties of the unique solution of a mean-field -SDE. More precisely, we consider a mean-field -SDE with square-integrable random initial condition and…
Detecting asset price bubbles using deep learning
Francesca Biagini, Lukas Gonon, Andrea Mazzon +1
In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-indep…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic c…