The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new machine learning-based method is obtained by solving a stochastic weighted minimization with stochastic gradient descent which is inspired by a high-order weak approximation scheme for stochastic differential equations (SDEs) with Malliavin weights. Then solutions to high-dimensional Kolmogorov PDEs or expectations of functionals of solutions to high-dimensional SDEs are accurately approximated without suffering from the curse of dimensionality. Numerical examples for PDEs and SDEs up to 100 dimensions are shown by using second and third-order discretization schemes in order to demonstrate the effectiveness of our method.

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into two parts, namely "dominant" linear and "small" nonlinear PDEs. Then, we apply a Deep BSDE solver with a new control variate method to solve those PDEs, where approximations based on an asymptotic expansion technique are effectively applied to the linear part and also used as control variates for the nonlinear part. Moreover, our theoretical result indicates that errors of the proposed method become much smaller than those of the original Deep BSDE solver. Finally, we show numerical experiments to demonstrate the validity of our method, which is consistent with the theoretical result in this paper.

We use the superposition of the Levy processes to optimize the classic BN-S model. Considering the frequent fluctuations of price parameters difficult to accurately estimate in the model, we preprocess the price data based on fuzzy theory. The price of S&P500 stock index options in the past ten years are analyzed, and the deterministic fluctuations are captured by machine learning methods. The results show that the new model in a fuzzy environment solves the long-term dependence problem of the classic model with fewer parameter changes, and effectively analyzes the random dynamic characteristics of stock index option price time series.

An energy storage technology is valuable if it makes energy systems cheaper. Traditional ways to improve storage technologies are to reduce their costs; however, the cheapest energy storage is not always the most valuable in energy systems. This paper reviews techno-economic storage valuation methods and expands them by the new "market potential method" which derives a system-value by examining the capacities obtained from a long-term investment planning optimisation. We apply and compare this method to other cost metrics in a renewables-based European power system model, covering diverse energy storage technologies. We find that characteristics of high-cost hydrogen storage can be equally or even more valuable than low-cost hydrogen storage. Additionally, we show that modifying the freedom of storage sizing and component interactions can make the energy system 10% cheaper and impact the value of technologies. The results suggest to look beyond the pure cost reduction paradigm and focus on developing technologies with value approaches that can lead to cheaper electricity systems in future. One practical and useful value method to guide energy storage innovation could be the market potential method.

We call an investment strategy survival, if an agent who uses it maintains a non-vanishing share of market wealth over the infinite time horizon. In a discrete-time multi-agent model with endogenous asset prices determined through a short-run equilibrium of supply and demand, we show that a survival strategy can be constructed as follows: an agent should assume that only their actions determine the prices and use a growth optimal (log-optimal) strategy with respect to these prices, disregarding the actual prices. Then any survival strategy turns out to be close to this strategy asymptotically. The main results are obtained under the assumption that the assets are short-lived.

A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyze how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market, which enables institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations.

We adopt deep learning models to directly optimise the portfolio Sharpe ratio. The framework we present circumvents the requirements for forecasting expected returns and allows us to directly optimise portfolio weights by updating model parameters. Instead of selecting individual assets, we trade Exchange-Traded Funds (ETFs) of market indices to form a portfolio. Indices of different asset classes show robust correlations and trading them substantially reduces the spectrum of available assets to choose from. We compare our method with a wide range of algorithms with results showing that our model obtains the best performance over the testing period, from 2011 to the end of April 2020, including the financial instabilities of the first quarter of 2020. A sensitivity analysis is included to understand the relevance of input features and we further study the performance of our approach under different cost rates and different risk levels via volatility scaling.

We show that disentangling sentiment-induced biases from fundamental expectations significantly improves the accuracy and consistency of probabilistic forecasts. Using data from 1994 to 2017, we analyze 15 stochastic models and risk-preference combinations and in all possible cases a simple behavioral transformation delivers substantial forecast gains. Our results are robust across different evaluation methods, risk-preference hypotheses and sentiment calibrations, demonstrating that behavioral effects can be effectively used to forecast asset prices. Further analyses confirm that our real-world densities outperform densities recalibrated to avoid past mistakes and improve predictive models where risk aversion is dynamically estimated from option prices.

Standard approaches to the theory of financial markets are based on equilibrium and efficiency. Here we develop an alternative based on concepts and methods developed by biologists, in which the wealth invested in a financial strategy is like the abundance of a species. We study a toy model of a market consisting of value investors, trend followers and noise traders. We show that the average returns of strategies are strongly density dependent, i.e. they depend on the wealth invested in each strategy at any given time. In the absence of noise the market would slowly evolve toward an efficient equilibrium, but the statistical uncertainty in profitability (which is adjusted to match real markets) makes this noisy and uncertain. Even in the long term, the market spends extended periods of time away from perfect efficiency. We show how core concepts from ecology, such as the community matrix and food webs, give insight into market behavior. The wealth dynamics of the market ecology explain how market inefficiencies spontaneously occur and gives insight into the origins of excess price volatility and deviations of prices from fundamental values.

Limited-information inference on New Keynesian Phillips Curves (NKPCs) and other single-equation macroeconomic relations is characterised by weak and high-dimensional instrumental variables (IVs). Beyond the efficiency concerns previously raised in the literature, I show by simulation that ad-hoc selection procedures can lead to substantial biases in post-selection inference. I propose a Sup Score test that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that increases exponentially with the sample size. Conducting inference on a standard NKPC with 359 IVs and 179 observations, I find substantially wider confidence sets than those commonly found.

The Glosten-Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szil\'ard information engine by {\em i)} showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and {\em ii)} defining a market analogue of the physical temperature from the analysis of the distribution of market orders. Then we show that the expected gain of informed traders is bounded above by the product of this market temperature with the amount of information that informed traders have, in exact analogy with the corresponding formula for the maximal expected amount of work that can be extracted from a cycle of the information engine. This suggests that recent ideas from information thermodynamics may shed light on financial markets, and lead to generalised inequalities, in the spirit of the extended second law of thermodynamics.

Regional quarantine policies, in which a portion of a population surrounding infections are locked down, are an important tool to contain disease. However, jurisdictional governments -- such as cities, counties, states, and countries -- act with minimal coordination across borders. We show that a regional quarantine policy's effectiveness depends upon whether (i) the network of interactions satisfies a balanced-growth condition, (ii) infections have a short delay in detection, and (iii) the government has control over and knowledge of the necessary parts of the network (no leakage of behaviors). As these conditions generally fail to be satisfied, especially when interactions cross borders, we show that substantial improvements are possible if governments are outward-looking and proactive: triggering quarantines in reaction to neighbors' infection rates, in some cases even before infections are detected internally. We also show that even a few lax governments -- those that wait for nontrivial internal infection rates before quarantining -- impose substantial costs on the whole system. Our results illustrate the importance of understanding contagion across policy borders and offer a starting point in designing proactive policies for decentralized jurisdictions.

This paper aims at proposing a model representing individuals' welfare using Sen's capability approach (CA). It is the first step of an attempt to measure the negative impact caused by the damage at a Common on a given population's welfare, and widely speaking, a first step into modelling collective threat. The CA is a multidimensional representation of persons' well-beings which account for human diversity. It has received substantial attention from scholars from different disciplines such as philosophy, economics and social scientist. Nevertheless, there is no empirical work that really fits the theoretical framework. Our goal is to show that the capability approach can be very useful for decision aiding, especially if we fill the gap between the theory and the empirical work; thus we will propose a framework that is both usable and a close representation of what capability is.

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience in behavioral economics. On strength of probabilistic potential theory, we establish the existence of an optimal equilibrium among a sufficiently large collection of equilibria, consisting of finely closed equilibria satisfying a boundary condition. This generalizes the existence of optimal equilibria for one-dimensional stopping problems in prior literature.

Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singular perturbation methods. We prove, by constructing sub- and super-solutions, that the approximations are accurate to the specified order. Finally, we perform some numerical experiments to illustrate the effect that stochastic trading frictions have on optimal trading.

We consider an optimal investment problem to maximize expected utility of the terminal wealth, in an illiquid market with search frictions and transaction costs. In the market model, an investor's attempt of transaction is successful only at arrival times of a Poisson process, and the investor pays proportional transaction costs when the transaction is successful. We characterize the no-trade region describing the optimal trading strategy. We provide asymptotic expansions of the boundaries of the no-trade region and the value function, for small transaction costs. The asymptotic analysis implies that the effects of the transaction costs are more pronounced in the market with less search frictions.

The difference in COVID 19 death rates across political regimes has caught a lot of attention. The "efficient autocracy" view suggests that autocracies may be more efficient at putting in place policies that contain COVID 19 spread. On the other hand, the "biasing autocracy" view underlines that autocracies may be under reporting their COVID 19 data. We use fixed effect panel regression methods to discriminate between the two sides of the debate. Our results show that a third view may in fact be prevailing: once pre-determined characteristics of countries are accounted for, COVID 19 death rates equalize across political regimes. The difference in death rate across political regime seems therefore to be primarily due to omitted variable bias.

While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven, spatial modeling of individuals to the simplest configurations and parameters: an equal resource opportunity landscape with equally capable individuals; and asks the question, "Will valid complex population and inequality dynamics emerge from this simple economic model?" Two foraging economies are modeled: subsistence and surplus. The resulting, emergent population dynamics are characterized by their sensitivities to agent and landscape parameters. The various steady and oscillating regimes of single-species population dynamics are generated by appropriate selection of model growth parameters. These emergent dynamics are shown to be consistent with the equation-based, continuum modeling of single-species populations in biology and ecology. The intrinsic growth rates, carry capacities, and delay parameters of these models are implied for these simple economies. Aggregate measures of individual distributions are used to understand the sensitivities to model parameters. New local measures are defined to describe complex behaviors driven by spatial effects, especially extinctions. This simple economic model is shown to generate significantly complex population and inequality dynamics. Model parameters generating the intrinsic growth rate have strong effects on these dynamics, including large variations in inequality. Significant inequality effects are shown to be caused by birth costs above and beyond their contribution to the intrinsic growth rate. The highest levels of inequality are found during the initial non-equilibrium period and are driven by factors different than those driving steady state inequality.

The problem of pricing utility-scale energy storage resources (ESRs) in the real-time electricity market is considered. Under a rolling-window dispatch model where the operator centrally dispatches generation and consumption under forecasting uncertainty, it is shown that almost all uniform pricing schemes, including the standard locational marginal pricing (LMP), result in lost opportunity costs that require out-of-the-market settlements. It is also shown that such settlements give rise to disincentives for generating firms and storage participants to bid truthfully, even when these market participants are rational price-takers in a competitive market. Temporal locational marginal pricing (TLMP) is proposed for ESRs as a generalization of LMP to an in-market discriminative form. TLMP is a sum of the system-wide energy price, LMP, and the individual state-of-charge price. It is shown that, under arbitrary forecasting errors, the rolling-window implementation of TLMP eliminates the lost opportunity costs and provides incentives to price-taking firms to bid truthfully with their marginal costs. Numerical examples show insights into the effects of uniform and non-uniform pricing mechanisms on dispatch following and truthful bidding incentives.

In the era of a growing population, systemic change of the world, and rising risk of crises, humanity has been facing an unprecedented challenge of resource scarcity. Confronting and addressing the issues concerning the scarce resource's conservation, competition, and stimulation by grappling their characters and adopting viable policy instruments calls the decision-makers' attention to a paramount priority. In this paper, we develop the first general decentralized cross-sector supply chain network model that captures the unique features of the scarce resources under fiscal-monetary policies. We formulate the model as a network equilibrium problem with finite-dimensional variational inequality theories. We then characterize the network equilibrium with a set of classic theoretical properties, as well as some novel properties (with $\lambda_{min}$) that are new to the literature of network games application. Lastly, we provide a series of illustrative examples, including a medical glove supply chain, to showcase how our model can be used to investigate the efficacy of the imposed policies in relieving the supply chain distress and stimulating welfare. Our managerial insights encompass the industry profit and social benefit vis-\`a-vis the resource availability and policy instrument design.

We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to retrieving the optimal Q-function at any time step, one can also price the contract at inception. We first discuss the standard setting with one exercise right, and later extend this framework to the case of multiple stopping opportunities in the presence of constraints. We propose to approximate the Q-function with a deep neural network, which does not require the specification of basis functions as in the least-squares Monte Carlo framework and is scalable to higher dimensions. We derive a lower bound on the option price obtained from the trained neural network and an upper bound from the dual formulation of the stopping problem, which can also be expressed in terms of the Q-function. Our methodology is illustrated with examples covering the pricing of swing options.

We describe an optimization-based tax-aware portfolio construction method that adds tax liability to standard Markowitz-based portfolio construction. Our method produces a trade list that specifies the number of shares to buy of each asset and the number of shares to sell from each tax lot held. To avoid wash sales (in which some realized capital losses are disallowed), we assume that we trade monthly, and cannot simultaneously buy and sell the same asset.

The tax-aware portfolio construction problem is not convex, but it becomes convex when we specify, for each asset, whether we buy or sell it. It can be solved using standard mixed-integer convex optimization methods at the cost of very long solve times for some problem instances. We present a custom convex relaxation of the problem that borrows curvature from the risk model. This relaxation can provide a good approximation of the true tax liability, while greatly enhancing computational tractability. This method requires the solution of only two convex optimization problems: the first determines whether we buy or sell each asset, and the second generates the final trade list. In our numerical experiments, our method almost always solves the nonconvex problem to optimality, and when it does not, it produces a trade list very close to optimal. Backtests show that the performance of our method is indistinguishable from that obtained using a globally optimal solution, but with significantly reduced computational effort.

This essay investigates the role of cost in the development and production of secure integrated circuits. Initially, I make a small introduction on hardware attacks on smart cards and some of the reasons behind them. Subsequently, I introduce the production phases of chips that are integrated to smart cards and try to identify the costs affecting each one of them. I proceed to identify how adding security features on such integrated circuits may affect the costs of their development and production. I then make a more thorough investigation on the costs of developing a hardware attack for such chips and try to estimate the potential damages and losses of such an attack. I also go on to examine potential ways of reducing the cost of production for secure chips, while identifying the difficulties in adopting them.

This essay ends with the conclusion that adding security features to chips meant to be used for secure applications is well worth it, because the costs of developing attacks are of comparable amounts to the costs of developing and producing a chip and the potential damages and losses caused by such attacks can be way higher than these costs. Therefore, although the production and development of integrated circuits come at a certain cost and security introduces further additional costs, security is inherently unavoidable in such chips. Finally, I additionally identify that security is an evolving concept and does not aim to make a chip totally impenetrable, as this may be impossible, but to lower the potential risks, including that of being compromised, to acceptable levels. Thus, a balance needs be found between the level of security and the levels of cost and risk.

This study more complex digital platforms in early stages in the two-sided market to produce powerful network effects. In this study, I use Transfer Entropy to look for super users who connect hominids in different networks to achieve higher network effects in the digital platform in the two-sided market, which has recently become more complex. And this study also aims to redefine the decision criteria of product managers by helping them define users with stronger network effects. With the development of technology, the structure of the industry is becoming more difficult to interpret and the complexity of business logic is increasing. This phenomenon is the biggest problem that makes it difficult for start-ups to challenge themselves. I hope this study will help product managers create new digital economic networks, enable them to make prioritized, data-driven decisions, and find users who can be the hub of the network even in small products.

We examine the pricing of a horizon specific uncertainty network risk, extracted from option implied variances on exchange rates, in the cross-section of currency returns. Buying currencies that are receivers and selling currencies that are transmitters of short-term shocks exhibits a high Sharpe ratio and yields a significant alpha when controlling for standard dollar, carry trade, volatility, variance risk premium and momentum strategies. This profitability stems primarily from the causal nature of shock propagation and not from contemporaneous dynamics. Shock propagation at longer horizons is priced less, indicating a downward-sloping term structure of uncertainty network risk in currency markets.

We extend the Hierarchical Factor Segmentation(HFS) algorithm for discovering multiple volatility states process hidden within each individual S&P500 stock's return time series. Then we develop an associative measure to link stocks into directed networks of various scales of associations. Such networks shed lights on which stocks would likely stimulate or even promote, if not cause, volatility on other linked stocks. Our computing endeavors starting from encoding events of large return on the original time axis to transform the original return time series into a recurrence-time process on discrete-time-axis. By adopting BIC and clustering analysis, we identify potential multiple volatility states, and then apply the extended HFS algorithm on the recurrence time series to discover its underlying volatility state process. Our decoding approach is found favorably compared with Viterbi's in experiments involving both light and heavy tail distributions. After recovering the volatility state process back to the original time-axis, we decode and represent stock dynamics of each stock. Our measurement of association is measured through overlapping concurrent volatility states upon a chosen window. Consequently, we establish data-driven associative networks for S&P500 stocks to discover their global dependency relational groupings with respect to various strengths of links.

The objective of this study is to examine spatial patterns of impacts and recovery of communities based on variances in credit card transactions. Such variances could capture the collective effects of household impacts, disrupted accesses, and business closures, and thus provide an integrative measure for examining disaster impacts and community recovery in disasters. Existing studies depend mainly on survey and sociodemographic data for disaster impacts and recovery effort evaluations, although such data has limitations, including large data collection efforts and delayed timeliness results. In addition, there are very few studies have concentrated on spatial patterns and disparities of disaster impacts and short-term recovery of communities, although such investigation can enhance situational awareness during disasters and support the identification of disparate spatial patterns of disaster impacts and recovery in the impacted regions. This study examines credit card transaction data Harris County (Texas, USA) during Hurricane Harvey in 2017 to explore spatial patterns of disaster impacts and recovery during from the perspective of community residents and businesses at ZIP code and county scales, respectively, and to further investigate their spatial disparities across ZIP codes. The results indicate that individuals in ZIP codes with populations of higher income experienced more severe disaster impact and recovered more quickly than those located in lower-income ZIP codes for most business sectors. Our findings not only enhance the understanding of spatial patterns and disparities in disaster impacts and recovery for better community resilience assessment, but also could benefit emergency managers, city planners, and public officials in harnessing population activity data, using credit card transactions as a proxy for activity, to improve situational awareness and resource allocation.