The aim of this paper is to build dependent stochastic processes using the notion of self-decomposability in order to model dependence across different markets and extend some recently proposed multivariate L\'evy models based on subordination. Consequently, we study the properties of such processes, derive closed form expressions for characteristic function and linear correlation coefficient and develop Monte Carlo schemes for their simulation. These results are instrumental to calibrate the models on power and gas energy European markets and to price spread options written on different underlying assets using Monte Carlo and Fourier techniques.

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 empirically investigate the functional link between the variance swap rate and the spot variance. Using S\&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kallsen et al. (2011) in the context of exponentially affine stochastic volatility models. Tests on yearly subsamples suggest that exponentially mean-reverting variance models provide a good fit during periods of extreme volatility, while polynomial models, introduced in Cuchiero (2011), are suited for years characterized by more frequent price jumps.

This paper develops a search problem where a consumer initially is aware of only a few products. To find a good match, the consumer sequentially decides between searching among alternatives he is already aware of and discovering more products. I show that the optimal policy for this search and discovery problem is fully characterized by tractable reservation values. Moreover, I prove that a predetermined index fully specifies the purchase decision of a consumer following the optimal search policy. Finally, a comparison highlights differences to classical random and directed search.

Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these extremes. We find that the waiting time between consecutive extremes (recurrence interval) follow a $q$-exponential distribution and the sizes of extremes above the thresholds (exceeding size) conform to a generalized Pareto distribution. We also find that there is a significant correlation between recurrence intervals and exceeding sizes. We thus model the joint distribution of recurrence intervals and exceeding sizes through connecting the two corresponding marginal distributions with the Frank and AMH copula functions, and apply this joint distribution to estimate the hazard probability to observe another extreme in $\Delta t$ time since the last extreme happened $t$ time ago. Furthermore, an extreme predicting model based on RIA-EVT-Copula is proposed by applying a decision-making algorithm on the hazard probability. Both in-sample and out-of-sample tests reveal that this new extreme forecasting framework has better performance in prediction comparing with the forecasting model based on the hazard probability only estimated from the distribution of recurrence intervals. Our results not only shed a new light on understanding the occurring pattern of extremes in financial markets, but also improve the accuracy to predict financial extremes for risk management.

We consider the problem of neural network training in a time-varying context. Machine learning algorithms have excelled in problems that do not change over time. However, problems encountered in financial markets are often non-stationary. We propose the online early stopping algorithm and show that a neural network trained using this algorithm can track a function changing with unknown dynamics. We applied the proposed algorithm to the stock return prediction problem studied in Gu et al. (2019) and achieved mean rank correlation of 4.69%, almost twice as high as the expanding window approach. We also show that prominent factors, such as the size effect and momentum, exhibit time varying stock return predictiveness.