Optimal execution with rough path signatures

We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of the optimisation problem, we are able to calculate an optimal solution for the trading speed in the space of linear functions on a truncation of the signature of the price process. We provide strong numerical evidence illustrating the accuracy and flexibility of the approach. Our numerical investigation both examines cases where exact solutions are known, demonstrating that the method accurately approximates these solutions, and models where exact solutions are not known. In the latter case, we obtain favourable comparisons with standard execution strategies

Anomaly detection on streamed data

We introduce powerful but simple methodology for identifying anomalous observations against a corpus of `normal' observations. All data are observed through a vector-valued feature map. Our approach depends on the choice of corpus and that feature map but is invariant to affine transformations of the map and has no other external dependencies, such as choices of metric; we call it conformance. Applying this method to (signatures) of time series and other types of streamed data we provide an effective methodology of broad applicability for identifying anomalous complex multimodal sequential data. We demonstrate the applicability and effectiveness of our method by evaluating it against multiple data sets. Based on quantifying performance using the receiver operating characteristic (ROC) area under the curve (AUC), our method yields an AUC score of 98.9\% for the PenDigits data set; in a subsequent experiment involving marine vessel traffic data our approach yields an AUC score of 89.1\%. Based on comparison involving univariate time series from the UEA \& UCR time series repository with performance quantified using balanced accuracy and assuming an optimal operating point, our approach outperforms a state-of-the-art shapelet method for 19 out of 28 data sets

A data-driven market simulator for small data environments

The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be applied. On the one hand, this flexibility allows the method to be tailored to specific problems, but on the other hand, can make precise application challenging. This paper makes two contributions. First, the variations on the signature method are unified into a general approach, the \emph{generalised signature method}, of which previous variations are special cases. A primary aim of this unifying framework is to make the signature method more accessible to any machine learning practitioner, whereas it is now mostly used by specialists. Second, and within this framework, we derive a canonical collection of choices that provide a domain-agnostic starting point. We derive these choices as a result of an extensive empirical study on 26 datasets and go on to show competitive performance against current benchmarks for multivariate time series classification. Finally, to ease practical application, we make our techniques available as part of the open-source [redacted] project

Witnessing the key early phase of quasar evolution: an obscured AGN pair in the interacting galaxy IRAS 20210+1121

We report the discovery of an active galactic nucleus (AGN) pair in the interacting galaxy system IRAS 20210+1121 at z = 0.056. An XMM-Newton observation reveals the presence of an obscured (Nh ~ 5 x 10^{23} cm^-2), Seyfert-like (L_{2-10 keV} = 4.7 x 10^{42} erg/s) nucleus in the northern galaxy, which lacks unambiguous optical AGN signatures. Our spectral analysis also provides strong evidence that the IR-luminous southern galaxy hosts a Type 2 quasar embedded in a bright starburst emission. In particular, the X-ray primary continuum from the nucleus appears totally depressed in the XMM-Newton band as expected in case of a Compton-Thick absorber, and only the emission produced by Compton scattering ('reflection') of the continuum from circumnuclear matter is seen. As such, IRAS 20210+1121 seems to provide an excellent opportunity to witness a key, early phase in the quasar evolution predicted by the theoretical models of quasar activation by galaxy collisions.Comment: Accepted for publication in The Astrophysical Journal Letter

Bitcoin private key locked transactions

Bitcoin smart contracts allow the development of new protocols on top of Bitcoin itself. This usually involves the definition of complex scripts, far beyond the requirement of a single signature. In this paper we introduce the concept of private key locked transactions, a novel type of transactions that allows the atomic verification of a given private key (belonging to an asymmetric key pair) during the payment execution