Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens among participants. The complete historical bookkeeping and its wide availability opens up an unprecedented possibility, i.e., that of understanding the evolution of their network structure while gaining useful insight on the relationships between user behaviour and cryptocurrency pricing in exchange markets. In this contribution we review some of the most recent results concerning the structural properties of Bitcoin Transaction Networks, a generic name referring to a set of different constructs: the Bitcoin Address Network, the Bitcoin User Network and the Bitcoin Lightning Network. A common picture that emerges out of analysing them all is that of a system growing over time, which becomes increasingly sparse, and whose structural organization at the mesoscopic level is characterised by the presence of a statistically-significant core-periphery structure. Such a peculiar topology is matched by a highly unequal distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralised system at different levels.

Within national and international innovation systems a pandemic calls for large-scale action by many actors across sectors, to mobilise resources, developing and manufacturing Crisis-Critical Products (CC-Products) efficiently and in the huge quantities needed. Nowadays, this also includes digital innovations from complex epidemiological models, AI, to open data platforms for prevention, diagnostic and treatment. Amongst the many challenges during a pandemic, innovation and manufacturing stakeholders find themselves engaged in new relationships, and are likely to face intellectual property (IP) related challenges. This paper adopts an IP perspective on the COVID-19 pandemic to identify pandemic related IP considerations and IP challenges. The focus is on challenges related to research, development and urgent upscaling of capacity to manufacture CC-Products in the huge volumes suddenly in demand. Its purpose is to provide a structure for steering clear of IP challenges to avoid delays in fighting a pandemic. We identify 4 stakeholder groups concerned with IP challenges: (i) governments, (ii) organisations owning existing Crisis-Critical IP, described as incumbents in Crisis-Critical Sectors (CC-Sectors), (iii) manufacturing firms from other sectors normally not producing CC-Products suddenly rushing into CC-Sectors to support the manufacturing of CC-Products (new entrants), and (iv) voluntary grassroot initiatives that are formed during a pandemic. This paper discusses IP challenges related to the development and manufacturing of technologies and products for (i) prevention (of spread), (ii) diagnosis of infected patients and (iii) the development of treatments. We offer an initial discussion of potential response measures to reduce IP associated risks among industrial stakeholders during a pandemic.

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum principle. This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. We present a number of numerical solutions of the system under a variety of scenarios.

Mobile phone data -- with file sizes scaling into terabytes -- easily overwhelm the computational capacity available to some researchers. Moreover, for ethical reasons, data access is often granted only to particular subsets, restricting analyses to cover single days, weeks, or geographical areas. Consequently, it is frequently impossible to set a particular analysis or event in its context and know how typical it is, compared to other days, weeks or months. This is important for academic referees questioning research on mobile phone data and for the analysts in deciding how to sample, how much data to process, and which events are anomalous. All these issues require an understanding of variability in Big Data to answer the question of how average is average? This paper provides a method, using a large mobile phone dataset, to answer these basic but necessary questions. We show that file size is a robust proxy for the activity level of phone users by profiling the temporal variability of the data at an hourly, daily and monthly level. We then apply time-series analysis to isolate temporal periodicity. Finally, we discuss confidence limits to anomalous events in the data. We recommend an analytical approach to mobile phone data selection which suggests that ideally data should be sampled across days, across working weeks, and across the year, to obtain a representative average. However, where this is impossible, the temporal variability is such that specific weekdays' data can provide a fair picture of other days in their general structure.

We propose a general strategy for estimating treatment effects, in contexts where the only source of exogenous variation is a sequence of aggregate time-series shocks. We start by arguing that commonly used estimation procedures tend to ignore the crucial time-series aspects of the data. Next, we develop a graphical tool and a novel test to illustrate the issues of the design using data from influential studies in development economics and macroeconomics. Motivated by these studies, we construct a new estimator, which is based on the time-series model for the aggregate shock. We analyze the statistical properties of our estimator in the practically relevant case, where both cross-sectional and time-series dimensions are of similar size. Finally, to provide causal interpretation for our estimator, we analyze a new causal model that allows for rich unobserved heterogeneity in potential outcomes and unobserved aggregate shocks.

We construct the term structure of the (forward-looking, US market) equity risk premium from SPX option chains. The method is "model-light". Risk-neutral probability densities are estimated by fitting $N$-component Gaussian mixture models to option quotes, where $N$ is a small integer (here 4 or 5). These densities are transformed to their real-world equivalents by exponential tilting with a single parameter: the Coefficient of Relative Risk Aversion $\kappa$. From history, I estimate $\kappa = 3 \pm 0.5$. From the inferred real-world densities, the equity risk premium is readily calculated. Three term structures serve as examples.

This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods.

Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. This allows us to connect the network structure to the popularity-vs-similarity model of Papdopoulos et al., which is based on the Poincar\'e disc model of hyperbolic geometry. We show that the latent dimensions of `popularity' and `similarity' in this model are strongly associated to systemic importance and to geographic subdivisions of the banking system. In a longitudinal analysis over the time span from 2014 to 2018 we find that the systemic importance of individual banks has remained rather stable, while the peripheral community structure exhibits more (but still moderate) variability.