The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Neural ordinary differential equations are an attractive option for modelling temporal
dynamics. However, a fundamental issue is that the solution to an ordinary differential …

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal
dynamics. However, a fundamental limitation has been that such models have typically been …

Generative adversarial networks (GANs) have been extremely successful in generating
samples, from seemingly high dimensional probability measures. However, these methods …

Synthetic data is an emerging technology that can significantly accelerate the development
and deployment of AI machine learning pipelines. In this work, we develop high-fidelity time …

Neural network based data-driven market simulation unveils a new and flexible way of
modelling financial time series without imposing assumptions on the underlying stochastic …

The universal approximation property of various machine learning models is currently only
understood on a case-by-case basis, limiting the rapid development of new theoretically …

Recently, there has been an increased interest in the development of kernel methods for
learning with sequential data. The signature kernel is a learning tool with the potential to …

We consider asset price models whose dynamics are described by linear functions of the
(time extended) signature of a primary underlying process, which can range from a (market …

We consider a stochastic volatility model where the dynamics of the volatility are described
by a linear function of the (time extended) signature of a primary process which is supposed …