We show the statistical properties of the most important cryptocurrencies, of which Bitcoin is the most prominent example. We characterize their exchange rates versus the US Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single...

Random measures are used to describe the evolution of the limit order book. A new model for limit order arrival is proposed which enables us to construct a model of the order book. Our model is flexible enough to be fitted to empirical observations. It turns out that the limit order book will be...

This paper studies a dynamic market microstructure model in which a strategic market maker competes with an informed trader. We include the presence of noise traders and limit order traders in our setup. Our model is a N-period model. We give necessary and sufficient conditions for an...

Since the early beginning of investing as it was commonly seen as a form of gambling for the rich and wealthy, the idea of Harry Markowitz was revolutionising the way of thinking and how portfolios should be constructed. However, today the traditional mean-variance portfolios are still not fully...

Is there an informational gain by training a Deep Reinforcement Learning agent for automated stock trading using other time series than the one to be traded? In this work, we implement a DRL algorithm in a solid framework within a model-free and actor-critic approach and learn it with 21 global...

Generative Adversarial Networks (GANs) have shown remarkable success as a framework for trainingmodels to produce realistic-looking data. In this work, we propose a GAN to produce realistic real-valued time series, with an emphasis on their application to financial data.Our aim is having a GAN,...

We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly...

With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms...