This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). Making use of Malliavin calculus, we recast the traditional Euler contributions from an expectation conditional to an event of zero probability to a ratio of conditional expectations, where both the numerator and the denominator's conditioning events have positive probability. For several different models we show empirically that the estimator using this novel representation has no perceivable bias and variance smaller than a standard estimator used in practice.

This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for semi-continuous viscosity sub- and supersolutions for PDEs with singular terminal value. Continuity of the viscosity solution is enough to carry out the verification argument.

Assessing the impacts of COVID-19 are of paramount importance for global sustainability. Using a coordinated set of high-resolution sectoral assessment tools, we report a decrease of 4.2% in global CO$_2$ emission in first quarter of 2020. Our emission estimates reflect near real time inventories of emissions from power generation, transportation, industry, international aviation and maritime sectors in 34 countries that account for >70% of world energy-related CO2 emissions in recent years. Regional variations in CO$_2$ emissions are significant, with a decrease in China (-9.3%), US (-3.0%), Europe (EU-27 & UK) (-3.3%) and India (-2.4%), respectively. The decline of short-lived gaseous pollutants, such as NO$_2$ concentration observed by Satellites (-25.73% for China, -4.76% for US) and ground observations (-23% for China) is consistent with the estimates based on energy activity (-23.94% for China, -3.52% for US), but the decline is not seen in satellite assessments of aerosol optical depth (AOD) or dry column CO$_2$ (XCO$_2$). With fast recovery and partial re-opening of national economies, our findings suggest that total annual emissions may drop far less than previously estimated (e.g., by 25% for China and more than 5% for the whole world). However, the longer-term effects on CO$_2$ emissions are unknown and should be carefully monitored using multiple measures.

We introduce Denise, a deep learning based algorithm for decomposing positive semidefinite matrices into the sum of a low rank plus a sparse matrix. The deep neural network is trained on a randomly generated dataset using the Cholesky factorization. This method, benchmarked on synthetic datasets as well as on some S&P500 stock returns covariance matrices, achieves comparable results to several state-of-the-art techniques, while outperforming all existing algorithms in terms of computational time. Finally, theoretical results concerning the convergence of the training are derived.

Quantitative risk management, particularly volatility forecasting, is critically important to traders, portfolio managers as well as policy makers. In this paper, we applied quantum reservoir computing for forecasting VIX (the CBOE volatility index), a highly non-linear and memory intensive `real-life' signal that is driven by market dynamics and trader psychology and cannot be expressed by a deterministic equation. As a first step, we lay out the systematic design considerations for using a NISQ reservoir as a computing engine (which should be useful for practitioners). We then show how to experimentally evaluate the memory capacity of various reservoir topologies (using IBM-Q's Rochester device) to identify the configuration with maximum memory capacity. Once the optimal design is selected, the forecast is produced by a linear combination of the average spin of a 6-qubit quantum register trained using VIX and SPX data from year 1990 onwards. We test the forecast performance over the sub-prime mortgage crisis period (Dec 2007 - Jun 2009). Our results show a remarkable ability to predict the volatility during the Great Recession using today's NISQs.

In this paper the general principles and categories of mixed economy that currently exist in almost all countries of the world are presented. The paper also presents an Advanced Model of Mixed Economy with Threshold (AMMET), which is characterized by a reduced value (approx. 10-15%) of the State and public sector participation in the national economy and proposes and analyzes an econophysics model for the mixed economy.

Proof-of-work blockchains need to be carefully designed so as to create the proper incentives for miners to faithfully maintain the network in a sustainable way. This paper describes how the economic engineering of the Conflux Network, a high throughput proof-of-work blockchain, leads to sound economic incentives that support desirable and sustainable mining behavior. In detail, this paper parameterizes the level of income, and thus network security, that Conflux can generate, and it describes how this depends on user behavior and "policy variables'' such as block and interest inflation. It also discusses how the underlying economic engineering design makes the Conflux Network resilient against double spending and selfish mining attacks.

We estimate the Lipschitz constants of the gradient of a deep neural network and the network itself with respect to the full set of parameters. We first develop estimates for a deep feed-forward densely connected network and then, in a more general framework, for all neural networks that can be represented as solutions of controlled ordinary differential equations, where time appears as continuous depth. These estimates can be used to set the step size of stochastic gradient descent methods, which is illustrated for one example method.

Negative reviews on e-commerce platforms, mainly in the form of texts, are posted by online consumers to express complaints about unsatisfactory experiences, providing a proxy of big data for sellers to consider improvements. However, the exact knowledge that lies beyond the negative reviewing still remains unknown. Aimed at a systemic understanding of how online consumers post negative reviews, using 1, 450, 000 negative reviews from JD.com, the largest B2C platform in China, the behavioral patterns from temporal, perceptional and emotional perspectives are comprehensively explored in the present study. Massive consumers behind these reviews across four sectors in the most recent 10 years are further split into five levels to reveal group discriminations at a fine resolution. Circadian rhythms of negative reviewing after making purchases were found, and the periodic intervals suggest stable habits in online consumption and that consumers tend to negatively review at the same hour of the purchase. Consumers from lower levels express more intensive negative feelings, especially on product pricing and seller attitudes, while those from upper levels demonstrate a stronger momentum of negative emotion. The value of negative reviews from higher-level consumers is thus unexpectedly highlighted because of less emotionalization and less biased narration, while the longer-lasting characteristic of these consumers' negative responses also stresses the need for more attention from sellers. Our results shed light on implementing distinguished proactive strategies in different buyer groups to help mitigate the negative impact due to negative reviews.

The real challenge in drone-logistics is to develop an economically-feasible Unmanned Aerial Mobility Network (UAMN). In this paper, we propose an integrated airport location (strategic decision) and routes planning (operational decision) optimization framework to minimize the total cost of the network, while guaranteeing flow constraints, capacity constraints, and electricity constraints. To facility expensive long-term infrastructure planning facing demand uncertainty, we develop a data-driven risk-averse two-stage stochastic optimization model based on the Wasserstein distance. We develop a reformulation technique which simplifies the worst-case expectation term in the original model, and obtain a fractable Min-Max solution procedure correspondingly. Using Lagrange multipliers, we successfully decompose decision variables and reduce the complexity of computation. To provide managerial insights, we design specific numerical examples. For example, we find that the optimal network configuration is affected by the "pooling effects" in channel capacities. A nice feature of our DRO framework is that the optimal network design is relatively robust under demand uncertainty. Interestingly, a candidate node without historical demand records can be chosen to locate an airport. We demonstrate the application of our model for a real medical resources transportation problem with our industry partner, collecting donated blood to a blood bank in Hangzhou, China.

For the sake of extracting hidden mutual and coupled information from possibly uncoupled time-series, we explored the profound measures of network science on time-series. Alongside common methods in time-series analysis of coupling between financial and economic markets, mapping coupled time-series onto networks is an outstanding measure to provide insight into hidden aspects embedded in couplings intrinsically. In this manner, we discretize the amplitude of coupled time-series and investigate relative simultaneous locations of the corresponding amplitudes (nodes). The transmissions between simultaneous amplitudes are clarified by edges in the network. In this sense, by segmenting magnitudes, the scaling features, volatilities' size and also the direction of the coupled amplitudes can be described. The frequency of occurrences of the coupled amplitudes is illustrated by the weighted edges, that is to say, some coupled amplitudes in the time-series can be identified as communities in the network. The results show that despite apparently uncoupled joint probabilities, the couplings possess some aspects which diverge from random Gaussian noise. Thereby, with the aid of the network's topological and statistical measurements, we distinguished basic structures of coupling of cross-market networks. Meanwhile, it was discovered that even two possibly known uncoupled markets may possess coupled patterns with each other. Thereby, those markets should be examined as coupled and weakly coupled markets!

Scaling and multiscaling financial time series have been widely studied in the literature. The research on this topic is vast and still flourishing. One way to analyse the scaling properties of time series is through the estimation of scaling exponents. These exponents are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviours in time series. In the literature, several methods have been proposed to study the multiscaling property and in this paper we use the generalized Hurst exponent (GHE). On the base of this methodology, we propose a novel statistical procedure to robustly estimate and test the multiscaling property and we name it RNSGHE. This methodology, together with a combination of t-tests and F-tests to discriminated between real and spurious scaling. Moreover, we also introduce a new methodology to estimate the optimal aggregation time used in our methodology. We numerically validate our procedure on simulated time series using the Multifractal Random Walk (MRW) and then apply it to real financial data. We also present results for times series with and without anomalies and we compute the bias that such anomalies introduce in the measurement of the scaling exponents. Finally, we show how the use of proper scaling and multiscaling can ameliorate the estimation of risk measures such as Value at Risk (VaR). We also propose a methodology based on Monte Carlo simulation, that we name Multiscaling Value at Risk (MSVaR), which takes into account the statical properties of multiscaling time series. We show that by using this statistical procedure in combination with the robustly estimated multiscaling exponents, the one year forecasted MSVaR mimics the VaR on the annual data for the majority of the stocks analysed.

An income loss can have a negative impact on households, forcing them to reduce their consumption of some staple goods. This can lead to health issues and, consequently, generate significant costs for society. We suggest that consumers can, to prevent these negative consequences, buy insurance to secure sufficient consumption of a staple good if they lose part of their income. We develop a two-period/two-good principal-agent problem with adverse selection and endogenous reservation utility to model insurance with in-kind benefits. This model allows us to obtain semi-explicit solutions for the insurance contract and is applied to the context of fuel poverty. For this application, our model allows to conclude that, even in the least efficient scenario from the households point of view, i.e., when the insurance is provided by a monopoly, this mechanism improves significantly the living conditions of the riskiest households by ensuring them a sufficient consumption of energy.

This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in favour of the buyer as she only pays the premium when the market is in good condition for the protection against financial downturn. Under this framework, we look at an embedded option which gives the issuer an opportunity to call back the contract to a new one with reduced premium payment rate and slightly lower default coverage subject to paying a certain cost. We assume that the buyer is risk neutral investor trying to maximize the expected monetary value of the option over a class of stopping time. We discuss optimal solution to the stopping problem when the source of uncertainty of the asset price is modelled by L\'evy process with only downward jumps. Using recent development in excursion theory of L\'evy process, the results are given explicitly in terms of scale function of the L\'evy process. Furthermore, the value function of the stopping problem is shown to satisfy continuous and smooth pasting conditions regardless of regularity of the sample paths of the L\'evy process. Optimality and uniqueness of the solution are established using martingale approach for drawdown process and convexity of the scale function under Esscher transform of measure. Some numerical examples are discussed to illustrate the main results.

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level ($\beta$). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single $\beta$ and may output significantly different portfolios depending on how the $\beta$ is selected. We confirm even small changes in $\beta$ can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple $\beta$-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.

We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing maximally the company with less endowment is the optimal strategy for the collaboration if the Brownian motions are correlated and the transfer rate can exceed the drift rates. Moreover, we obtain an explicit formula for the minimal ruin probability in case of perfectly positively correlated Brownian motions where we also allow for different diffusion coefficients.

Tackling real-world socio-economic challenges requires designing and testing economic policies. However, this is hard in practice, due to a lack of appropriate (micro-level) economic data and limited opportunity to experiment. In this work, we train social planners that discover tax policies in dynamic economies that can effectively trade-off economic equality and productivity. We propose a two-level deep reinforcement learning approach to learn dynamic tax policies, based on economic simulations in which both agents and a government learn and adapt. Our data-driven approach does not make use of economic modeling assumptions, and learns from observational data alone. We make four main contributions. First, we present an economic simulation environment that features competitive pressures and market dynamics. We validate the simulation by showing that baseline tax systems perform in a way that is consistent with economic theory, including in regard to learned agent behaviors and specializations. Second, we show that AI-driven tax policies improve the trade-off between equality and productivity by 16% over baseline policies, including the prominent Saez tax framework. Third, we showcase several emergent features: AI-driven tax policies are qualitatively different from baselines, setting a higher top tax rate and higher net subsidies for low incomes. Moreover, AI-driven tax policies perform strongly in the face of emergent tax-gaming strategies learned by AI agents. Lastly, AI-driven tax policies are also effective when used in experiments with human participants. In experiments conducted on MTurk, an AI tax policy provides an equality-productivity trade-off that is similar to that provided by the Saez framework along with higher inverse-income weighted social welfare.

Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this question and proposes a new methodology to estimate the correlation matrix which doesn't depend on the chosen sample period. This new methodology is based on tensor factorization techniques. In particular, combining and normalizing factor components, we build a correlation matrix which shows emerging structural dependency properties not affected by the sample period. To retrieve the factor components, we propose a new tensor decomposition (which we name Slice-Diagonal Tensor (SDT) factorization) and compare it to the two most used tensor decompositions, the Tucker and the PARAFAC. We have that the new factorization is more parsimonious than the Tucker decomposition and more flexible than the PARAFAC. Moreover, this methodology applied to both simulated and empirical data shows results which are robust to two non-parametric tests, namely Kruskal-Wallis and Kolmogorov-Smirnov tests. Since the resulting correlation matrix features stability and emerging structural dependency properties, it can be used as alternative to other correlation matrices type of measures, including the Person correlation.

We develop a mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange. The multi-agent description leads to study the evolution over time of a system of kinetic equations for the wealth densities of susceptible, infectious and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology. Explicit calculations show that the spread of the disease seriously affects the distribution of wealth, which, unlike the situation in the absence of epidemics, can converge towards a stationary state with a bimodal form. Furthermore, simulations confirm the ability of the model to describe different phenomena characteristics of economic trends in situations compromised by the rapid spread of an epidemic, such as the unequal impact on the various wealth classes and the risk of a shrinking middle class.