We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters can be estimated by quasi likelihood maximization, without any interference from the baseline intensity. Consistency and asymptotic behavior of the estimators are given in several frameworks, and model selection is discussed with information criteria and penalization. The model is well-suited for high-frequency financial data: fitted models using easily interpretable covariates show an excellent agreement with empirical data. Extensive investigation on tick data consequently helps identifying trading signals and important factors determining the limit order book dynamics. We also illustrate the potential use of the framework for out-of-sample predictions.

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.

We develop an alternative theory to the aggregate matching function in which workers search for jobs through a network of firms: the labor flow network. The lack of an edge between two companies indicates the impossibility of labor flows between them due to high frictions. In equilibrium, firms' hiring behavior correlates through the network, generating highly disaggregated local unemployment. Hence, aggregation depends on the topology of the network in non-trivial ways. This theory provides new micro-foundations for the Beveridge curve, wage dispersion, and the employer-size premium. We apply our model to employer-employee matched records and find that network topologies with Pareto-distributed connections cause disproportionately large changes on aggregate unemployment under high labor supply elasticity.

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. This calls for a separate study of sublinear and superlinear expectations, since a change of sign does not convert one to the other in the set-valued setting. We identify the extremal expectations as those arising from the primal and dual representations of them. Several general construction methods for nonlinear expectations are presented and the corresponding duality representation results are obtained. On the application side, sublinear expectations are naturally related to depth trimming of multivariate samples, while superlinear ones can be used to assess utilities of multiasset portfolios.

Despite decades of research, the relationship between the quality of science and the value of inventions has remained unclear. We present the result of a large-scale matching exercise between the universes of 4.8 million patent families and 43 million publication records. We find a strong positive relationship between quality of scientific contributions referenced in patents and the value of the respective inventions. We rank patents by the quality of the science they are linked to. Strikingly, patents in the top decile are twice as valuable as patents in the bottom decile, which in turn are about as valuable as patents with no direct science link. We show this core result for various measures of science quality and patent value. The effect of science quality on patent value remains relevant even when science is linked indirectly, i.e., through other patents. Our findings imply that what is considered "excellent" within the science sector also leads to outstanding outcomes in the technological or commercial realm.