7 papers
Universal approximation with signatures of non-geometric rough paths
Mihriban Ceylan, Anna P. Kwossek, David J. Prömel
We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket t…
Pathwise analysis of log-optimal portfolios
Andrew L. Allan, Anna P. Kwossek, Chong Liu +1
Based on the theory of càdlàg rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories genera…
A rough path approach to pathwise stochastic integration à la Föllmer
Purba Das, Anna P. Kwossek, David J. Prömel
We develop a general framework for pathwise stochastic integration that extends Föllmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums an…
Stochastic differential equations driven by fractional Brownian motion: dependence on the Hurst parameter
Anna P. Kwossek, Andreas Neuenkirch, David J. Prömel
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose c…
Universal approximation property of neural stochastic differential equations
Anna P. Kwossek, David J. Prömel, Josef Teichmann
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neura…
Functional differential equations driven by càdlàg rough paths
Anna P. Kwossek, Andreas Neuenkirch, David J. Prömel
The existence of unique solutions is established for rough differential equations (RDEs) with path-dependent coefficients and driven by càdlàg rough paths. Moreover, it is shown th…