We consider a system consisting of multiple interdependent assets, and a set of defenders, each responsible for securing a subset of the assets against an attacker. The interdependencies between the assets are captured by an attack graph, where an edge from one asset to another indicates that if the former asset is compromised, an attack can be launched on the latter asset. Each edge has an associated probability of successful attack, which can be reduced via security investments by the defenders. In such scenarios, we investigate the security investments that arise under certain features of human decision-making that have been identified in behavioral economics. In particular, humans have been shown to perceive probabilities in a nonlinear manner, typically overweighting low probabilities and underweighting high probabilities. We show that suboptimal investments can arise under such weighting in certain network topologies. We also show that pure strategy Nash equilibria exist in settings with multiple (behavioral) defenders, and study the inefficiency of the equilibrium investments by behavioral defenders compared to a centralized socially optimal solution.

Once carbon emission neutrality and other sustainability goals have been achieved, a widespread assumption is that economic growth at current rates can be sustained beyond the 21st century. However, even if we achieve these goals, this article shows that the overall size of Earth's global economy is facing an upper limit purely due to energy and thermodynamic factors. For that, we break down global warming into two components: the greenhouse gas effect and heat dissipation from energy consumption related to economic activities. For the temperature increase due to greenhouse gas emissions, we take 2 {\deg}C and 5 {\deg}C as our lower and upper bounds. For the warming effect of heat dissipation related to energy consumption, we use a simplified model for global warming and an extrapolation of the historical correlation between global gross domestic product (GDP) and primary energy production. Combining the two effects, we set the acceptable global warming temperature limit to 7 {\deg}C above pre-industrial levels. We develop four scenarios, based on the viability of large-scale deployment of carbon-neutral energy sources. Our results indicate that for a 2% annual GDP growth, the upper limit will be reached at best within a few centuries, even in favorable scenarios where new energy sources such as fusion power are deployed on a massive scale. We conclude that unless GDP can be largely decoupled from energy consumption, thermodynamics will put a hard cap on the size of Earth's economy. Further economic growth would necessarily require expanding economic activities into space.

Our knowledge about the evolution of guarantee network in downturn period is limited due to the lack of comprehensive data of the whole credit system. Here we analyze the dynamic Chinese guarantee network constructed from a comprehensive bank loan dataset that accounts for nearly 80% total loans in China, during 01/2007-03/2012. The results show that, first, during the 2007-2008 global financial crisis, the guarantee network became smaller, less connected and more stable because of many bankruptcies; second, the stimulus program encouraged mutual guarantee behaviors, resulting in highly reciprocal and fragile network structure; third, the following monetary policy adjustment enhanced the resilience of the guarantee network by reducing mutual guarantees. Interestingly, our work reveals that the financial crisis made the network more resilient, and conversely, the government bailout degenerated network resilience. These counterintuitive findings can provide new insight into the resilience of real-world credit system under external shocks or rescues.

The lead-lag relationship plays a vital role in financial markets. It is the phenomenon where a certain price-series lags behind and partially replicates the movement of leading time-series. The present research proposes a new technique which helps better identify the lead-lag relationship empirically. Apart from better identifying the lead-lag path, the technique also gives a measure for adjudging closeness between financial time-series. Also, the proposed measure is closely related to correlation, and it uses Dynamic Programming technique for finding the optimal lead-lag path. Further, it retains most of the properties of a metric, so much so, it is termed as loose metric. Tests are performed on Synthetic Time Series (STS) with known lead-lag relationship and comparisons are done with other state-of-the-art models on the basis of significance and forecastability. The proposed technique gives the best results in both the tests. It finds paths which are all statistically significant, and its forecasts are closest to the target values. Then, we use the measure to study the topology evolution of the Foreign Exchange market, as the COVID-19 pandemic unfolds. Here, we study the FX currency prices of 29 prominent countries of the world. It is observed that as the crises unfold, all the currencies become strongly interlinked to each other. Also, USA Dollar starts playing even more central role in the FX market. Finally, we mention several other application areas of the proposed technique for designing intelligent systems.

We study the expected utility maximization problem of a large investor who is allowed to make transactions on a tradable asset in a financial market with endogenous permanent market impacts as suggested in [24] building on [6, 7]. The asset price is assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which is equivalent to a highly non-linear backward stochastic partial differential equation (BSPDE). Existence results can be achieved in the case where the driver function of the representative market maker is quadratic or the utility function of the large investor is exponential. Explicit examples are provided when the market is complete or the driver function is positively homogeneous.

We define a new family of multivariate stochastic processes over a finite time horizon that we call Generalised Liouville Processes (GLPs). GLPs are Markov processes constructed by splitting L\'evy random bridges into non-overlapping subprocesses via time changes. We show that the terminal values and the increments of GLPs have generalised multivariate Liouville distributions, justifying their name. We provide various other properties of GLPs and some examples.

Our study aims at quantifying the impact of climate change on corn farming in Ontario under several warming scenarios at the 2068 horizon. It is articulated around a discrete-time dynamic model of corn farm income with an annual time-step, corresponding to one agricultural cycle from planting to harvest. At each period, we compute the income given the corn yield, which is highly dependent on weather variables. We also provide a reproducible forecast of the yearly distribution of corn yield for 10 cities in Ontario. The price of corn futures at harvest time is taken into account and we fit our model by using 49 years of historical data. We then conduct out-of-sample Monte-Carlo simulations to obtain the farm income forecasts under a given climate change scenario.

We analyze an approach to managing the COVID-19 pandemic without shutting down the economy while staying within the capacity of the healthcare system. We base our analysis on a detailed heterogeneous epidemiological model, which takes into account different population groups and phases of the disease, including incubation, infection period, hospitalization, and treatment in the intensive care unit (ICU). We model the healthcare capacity as the total number of hospital and ICU beds for the whole country. We calibrate the model parameters to data reported in several recent research papers. For high- and low-risk population groups, we calculate the number of total and intensive care hospitalizations, and deaths as functions of time. The main conclusion is that countries, which enforce reasonable hygienic measures on time can avoid lockdowns throughout the pandemic provided that the number of spare ICU beds per million is above the threshold of about 100. In countries where the total number of ICU beds is below this threshold, a limited period quarantine to specific high-risk groups of the population suffices. Furthermore, in the case of an inadequate capacity of the healthcare system, we incorporate a feedback loop and demonstrate that quantitative impact of the lack of ICU units on the death curve. In the case of inadequate ICU beds, full- and partial-quarantine scenarios outcomes are almost identical, making it unnecessary to shut down the whole economy. We conclude that only a limited-time quarantine of the high-risk group might be necessary, while the rest of the economy can remain operational.

Stock price movement prediction is commonly accepted as a very challenging task due to the extremely volatile nature of financial markets. Previous works typically focus on understanding the temporal dependency of stock price movement based on the history of individual stock movement, but they do not take the complex relationships among involved stocks into consideration. However it is well known that an individual stock price is correlated with prices of other stocks. To address that, we propose a deep learning-based framework, which utilizes recurrent neural network (RNN) and graph convolutional network (GCN) to predict stock movement. Specifically, we first use RNN to model the temporal dependency of each related stock' price movement based on their own information of the past time slices, then we employ GCN to model the influence from involved stock based on three novel graphs which represent the shareholder relationship, industry relationship and concept relationship among stocks based on investment decisions. Experiments on two stock indexes in China market show that our model outperforms other baselines. To our best knowledge, it is the first time to incorporate multi-relationships among involved stocks into a GCN based deep learning framework for predicting stock price movement.

Neural networks have been used as a nonparametric method for option pricing and hedging since the early 1990s. Far over a hundred papers have been published on this topic. This note intends to provide a comprehensive review. Papers are compared in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Furthermore, related work and regularisation techniques are discussed.

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition which we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA$_1$ and NA$_1$ may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing. We also consider a financial market with semimartingales which does not need to have a num\'{e}raire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

A new semi-parametric Expected Shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two step estimation procedure. The first step involves the estimation of Value-at-Risk (VaR) at different levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantiles weighting structure is parsimoniously parameterized by means of a Beta function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler-Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using various data generating processes. Two forecasting studies with different out-of-sample sizes are conducted, one of which focuses on the 2008 Global Financial Crisis (GFC) period. The proposed models are applied to 7 stock market indices and their forecasting performances are compared to those of a range of parametric, non-parametric and semi-parametric models, including GARCH, Conditional AutoRegressive Expectile (CARE, Taylor 2008), joint VaR and ES quantile regression models (Taylor, 2019) and simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models.

This paper uses transaction data from a large bank in Scandinavia to estimate the effect of social distancing laws on consumer spending in the COVID-19 pandemic. The analysis exploits a natural experiment to disentangle the effects of the virus and the laws aiming to contain it: Denmark and Sweden were similarly exposed to the pandemic but only Denmark imposed significant restrictions on social and economic activities. We estimate that aggregate spending dropped by around 25 percent in Sweden and, as a result of the shutdown, by 4 additional percentage points in Denmark. This implies that most of the economic contraction is caused by the virus itself and occurs regardless of social distancing laws. The age gradient in the estimates suggest that social distancing reinforces the virus-induced drop in spending for low health-risk individuals but attenuates it for high-risk individuals by lowering the overall prevalence of the virus in the society.

In this paper we derive a efficient Monte Carlo approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models of Fouque \textit{et al}. Using the formulation of this pricing problem under the functional It\^o calculus framework and making use of Greek formulas from Malliavin calculus, we derive a representation for the first-order approximation of the price of path-dependent derivatives in the form $\mathbb{E}[\mbox{payoff} \times \mbox{weight}]$. The weight is known in closed form and depends only on the group market parameters arising from the calibration of the multiscale stochastic volatility to the market's implied volatility. Moreover, only simulations of the Black-Scholes model is required. We exemplify the method for a couple path-dependent derivatives.

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.

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in(0,1)$ as $n\to\infty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S\&P 500 constituents.