Deep learning (DL) has been applied extensively in a wide range of fields. However, it has been shown that DL models are susceptible to a certain kinds of perturbations called \emph{adversarial attacks}. To fully unlock the power of DL in critical fields such as financial trading, it is necessary to address such issues. In this paper, we present a method of constructing perturbed examples and use these examples to boost the robustness of the model. Our algorithm increases the stability of DL models for candlestick classification with respect to perturbations in the input data.

We study a new kind of non-zero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a representative downstream firm to produce a final consumption good. Both firms can influence the price of the commodity. By shutting down or increasing generation capacities, the upstream firm influences the price with impulses. By switching (or not) to a substitute, the downstream firm influences the drift of the commodity price process. We study the resulting impulse--regime switching game between the two firms, focusing on explicit threshold-type equilibria. Remarkably, this class of games naturally gives rise to multiple Nash equilibria, which we obtain via a verification based approach. We exhibit three types of equilibria depending on the ultimate number of switches by the downstream firm (zero, one or an infinite number of switches). We illustrate the diversification effect provided by vertical integration in the specific case of the crude oil market. Our analysis shows that the diversification gains strongly depend on the pass-through from the crude price to the gasoline price.

Tie-line scheduling in multi-area power systems in the US largely proceeds through a market-based mechanism called Coordinated Transaction Scheduling (CTS). We analyze this market mechanism through a game-theoretic lens. Our analysis characterizes the effects of market liquidity, market participants' forecasts about inter-area price spreads, transaction fees and interaction of CTS markets with financial transmission rights. Using real data, we empirically verify that CTS bidders can employ simple learning algorithms to discover Nash equilibria that support the conclusions drawn from the equilibrium analysis.

The robust PCA of high-dimensional matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, the algorithm must re-run each time a new matrix should be decomposed. Since these algorithms are computationally expensive, it is preferable to learn and store a function that instantaneously performs this decomposition when evaluated. Therefore, we introduce Denise, a deep learning-based algorithm for robust PCA of symmetric positive semidefinite matrices, which learns precisely such a function. Theoretical guarantees that Denise's architecture can approximate the decomposition function, to arbitrary precision and with arbitrarily high probability, are obtained. The training scheme is also shown to convergence to a stationary point of the robust PCA's loss-function. We train Denise on a randomly generated dataset, and evaluate the performance of the DNN on synthetic and real-world covariance matrices. Denise achieves comparable results to several state-of-the-art algorithms in terms of decomposition quality, but as only one evaluation of the learned DNN is needed, Denise outperforms all existing algorithms in terms of computation time.

Ageing populations in developing countries have spurred the introduction of public pension programs to preserve the standard of living for the elderly. The often-overlooked mechanism of intergenerational transfers, however, can dampen these intended policy effects as adult children who make income contributions to their parents could adjust their behavior to changes in their parents' income. Exploiting a unique policy intervention in China, we examine using a difference-in-difference-in-differences (DDD) approach how a new pension program impacts inter vivos transfers. We show that pension benefits lower the propensity of receiving transfers from adult children in the context of a large middle-income country and we also estimate a small crowd-out effect. Taken together, these estimates fit the pattern of previous research in high-income countries, although our estimates of the crowd-out effect are significantly smaller than previous studies in both high-income and middle-income countries.

Optimal trade execution is an important problem faced by essentially all traders. Much research into optimal execution uses stringent model assumptions and applies continuous time stochastic control to solve them. Here, we instead take a model free approach and develop a variation of Deep Q-Learning to estimate the optimal actions of a trader. The model is a fully connected Neural Network trained using Experience Replay and Double DQN with input features given by the current state of the limit order book, other trading signals, and available execution actions, while the output is the Q-value function estimating the future rewards under an arbitrary action. We apply our model to nine different stocks and find that it outperforms the standard benchmark approach on most stocks using the measures of (i) mean and median out-performance, (ii) probability of out-performance, and (iii) gain-loss ratios.

We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local) martingale deflators, we use a class of supermartingale deflators such that deflated wealth plus cumulative deflated consumption is a supermartingale for all admissible consumption plans. This yields a strong duality, because the enlarged dual domain of processes dominated by deflators is naturally closed, without invoking its closure. In this way we automatically reach the bipolar of the set of deflators. We complete this picture by proving that the set of processes dominated by local martingale deflators is dense in our dual domain, confirming that we have identified the natural dual space. In addition to the optimal consumption and deflator, we characterise the optimal wealth process. At the optimum, deflated wealth is a supermartingale and a potential, while deflated wealth plus cumulative deflated consumption is a uniformly integrable martingale. This is the natural generalisation of the corresponding feature in the terminal wealth problem, where deflated wealth at the optimum is a uniformly integrable martingale. We use no constructions involving equivalent local martingale measures. This is natural, given that such measures typically do not exist over the infinite horizon and that we are working under NUPBR, which does not require their existence. The structure of the duality proof reveals an interesting feature compared with the terminal wealth problem. There, the dual domain is $L^{1}$-bounded, but here the primal domain has this property, and hence many steps in the duality proof show a marked reversal of roles for the primal and dual domains, compared with the proofs of Kramkov and Schachermayer.

In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics of the interbank liabilities. Emphasis will be placed on the construction, existence, and uniqueness of the continuous-time framework and its formulation as a differential equation driven by the operating cash flows. Finally, the financial implications of time dynamics will be considered. The focus will be on how the dynamic clearing solutions differ from those of the static Eisenberg-Noe model.

This paper examines the pricing of dynamic horizon specific network risk in the cross-section of stock returns. We suggest how to track such dynamic network connections on a daily basis using time-varying parameter vector auto-regressions. Empirically, we characterize the short-term and long-term risks from a large-scale dynamic network on all S&P500 constituents' return volatilities. Consistent with theory, we show that stocks with high sensitivities to dynamic network risk earn lower returns. A two-standard deviation increase in long-term (short-term) network risk loadings associate with a 14.73% (12.96%) drop in annualized expected returns.

The fossil-fuel induced contribution to further warming over the 21st century will be determined largely by integrated CO2 emissions over time rather than the precise timing of the emissions, with a relation of near-proportionality between global warming and cumulative CO2 emissions. This paper examines optimal abatement pathways under an exogenous constraint on cumulative emissions. Least cost abatement pathways have carbon tax rising at the risk-free interest rate, but if endogenous learning or climate damage costs are included in the analysis, the carbon tax grows more slowly. The inclusion of damage costs in the optimization leads to a higher initial carbon tax, whereas the effect of learning depends on whether it appears as an additive or multiplicative contribution to the marginal cost curve. Multiplicative models are common in the literature and lead to delayed abatement and a smaller initial tax. The required initial carbon tax increases with the cumulative abatement goal and is higher for lower interest rates. Delaying the start of abatement is costly owing to the increasing marginal abatement cost. Lower interest rates lead to higher relative costs of delaying abatement because these induce higher abatement rates early on. The fraction of business-as-usual emissions (BAU) avoided in optimal pathways increases for low interest rates and rapid growth of the abatement cost curve, which allows a lower threshold global warming goal to become attainable without overshoot in temperature. Each year of delay in starting abatement raises this threshold by an increasing amount, because the abatement rate increases exponentially with time.

This article presents a deep reinforcement learning approach to price and hedge financial derivatives. This approach extends the work of Guo and Zhu (2017) who recently introduced the equal risk pricing framework, where the price of a contingent claim is determined by equating the optimally hedged residual risk exposure associated respectively with the long and short positions in the derivative. Modifications to the latter scheme are considered to circumvent theoretical pitfalls associated with the original approach. Derivative prices obtained through this modified approach are shown to be arbitrage-free. The current paper also presents a general and tractable implementation for the equal risk pricing framework inspired by the deep hedging algorithm of Buehler et al. (2019). An $\epsilon$-completeness measure allowing for the quantification of the residual hedging risk associated with a derivative is also proposed. The latter measure generalizes the one presented in Bertsimas et al. (2001) based on the quadratic penalty. Monte Carlo simulations are performed under a large variety of market dynamics to demonstrate the practicability of our approach, to perform benchmarking with respect to traditional methods and to conduct sensitivity analyses.

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.

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier-related inversion, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.

Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of market calibration is the computation of the variance of the asset. For energy commodities, it is common to adopt multi-factor linear models, whose variance obeys a matrix Lyapunov differential equation. In this paper, both analytical and numerical methods to derive the variance through a Lyapunov equation are discussed and compared in terms of computational efficiency. The Lyapunov approach illustrated herein is more straightforward than ad-hoc derivations found in the quantitative finance literature and can be readily extended by a practitioner to higher-dimensional models. A practical case study is presented, where the variance of a two-factor mean-reverting model is embedded into the Black formulae and the model parameters are then calibrated against listed options. In particular, the analytical and numerical method are compared, showing that the former makes the calibration 14 times faster. A Python implementation of the proposed procedures is available as open-source software on GitHub.

We propose an approach to generate realistic and high-fidelity stock market data based on generative adversarial networks (GANs). Our Stock-GAN model employs a conditional Wasserstein GAN to capture history dependence of orders. The generator design includes specially crafted aspects including components that approximate the market's auction mechanism, augmenting the order history with order-book constructions to improve the generation task. We perform an ablation study to verify the usefulness of aspects of our network structure. We provide a mathematical characterization of distribution learned by the generator. We also propose statistics to measure the quality of generated orders. We test our approach with synthetic and actual market data, compare to many baseline generative models, and find the generated data to be close to real data.

The design of integrated mobility-on-demand services requires jointly considering the interactions between traveler choice behavior and operators' operation policies to design a financially sustainable pricing scheme. However, most existing studies focus on the supply side perspective, disregarding the impact of customer choice behavior in the presence of co-existing transport networks. We propose a modeling framework for dynamic integrated mobility-on-demand service operation policy evaluation with two service options: door-to-door rideshare and rideshare with transit transfer. A new constrained dynamic pricing model is proposed to maximize operator profit, taking into account the correlated structure of different modes of transport. User willingness to pay is considered as a stochastic constraint, resulting in a more realistic ticket price setting while maximizing operator profit. Unlike most studies, which assume that travel demand is known, we propose a demand learning process to calibrate customer demand over time based on customers' historical purchase data. We evaluate the proposed methodology through simulations under different scenarios on a test network by considering the interactions of supply and demand in a multimodal market. Different scenarios in terms of customer arrival intensity, vehicle capacity, and the variance of user willingness to pay are tested. Results suggest that the proposed chance-constrained assortment price optimization model allows increasing operator profit while keeping the proposed ticket prices acceptable.

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.

Climate change has become intertwined with the global economy. Here, we describe the importance of inertia to continued growth in energy consumption. Drawing from thermodynamic arguments, and using 38 years of available statistics between 1980 to 2017, we find a persistent time-independent scaling between the historical time integral $W$ of world inflation-adjusted economic production $Y$, or $W\left(t\right) = \int_0^t Y\left(t'\right)dt'$, and current rates of world primary energy consumption $\mathcal E$, such that $\lambda = \mathcal{E}/W = 5.9\pm0.1$ Gigawatts per trillion 2010 US dollars. This empirical result implies that population expansion is a symptom rather than a cause of the current exponential rise in $\mathcal E$ and carbon dioxide emissions $C$, and that it is past innovation of economic production efficiency $Y/\mathcal{E}$ that has been the primary driver of growth, at predicted rates that agree well with data. Options for stabilizing $C$ are then limited to rapid decarbonization of $\mathcal E$ through sustained implementation of over one Gigawatt of renewable or nuclear power capacity per day. Alternatively, assuming continued reliance on fossil fuels, civilization could shift to a steady-state economy that devotes economic production exclusively to maintenance rather than expansion. If this were instituted immediately, continual energy consumption would still be required, so atmospheric carbon dioxide concentrations would not balance natural sinks until concentrations exceeded 500 ppmv, and double pre-industrial levels if the steady-state was attained by 2030.

Networked-guarantee loans may cause the systemic risk related concern of the government and banks in China. The prediction of default of enterprise loans is a typical extremely imbalanced prediction problem, and the networked-guarantee make this problem more difficult to solve. Since the guaranteed loan is a debt obligation promise, if one enterprise in the guarantee network falls into a financial crisis, the debt risk may spread like a virus across the guarantee network, even lead to a systemic financial crisis. In this paper, we propose an imbalanced network risk diffusion model to forecast the enterprise default risk in a short future. Positive weighted k-nearest neighbors (p-wkNN) algorithm is developed for the stand-alone case -- when there is no default contagious; then a data-driven default diffusion model is integrated to further improve the prediction accuracy. We perform the empirical study on a real-world three-years loan record from a major commercial bank. The results show that our proposed method outperforms conventional credit risk methods in terms of AUC. In summary, our quantitative risk evaluation model shows promising prediction performance on real-world data, which could be useful to both regulators and stakeholders.

Interest in predicting multivariate probability distributions is growing due to the increasing availability of rich datasets and computational developments. Scoring functions enable the comparison of forecast accuracy, and can potentially be used for estimation. A scoring function for multivariate distributions that has gained some popularity is the energy score. This is a generalization of the continuous ranked probability score (CRPS), which is widely used for univariate distributions. A little-known, alternative generalization is the multivariate CRPS (MCRPS). We propose a theoretical framework for scoring functions for multivariate distributions, which encompasses the energy score and MCRPS, as well as the quadratic score, which has also received little attention. We demonstrate how this framework can be used to generate new scores. For univariate distributions, it is well-established that the CRPS can be expressed as the integral over a quantile score. We show that, in a similar way, scoring functions for multivariate distributions can be "disintegrated" to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including those for densities and cumulative distributions. To compute the scoring functions, we propose a simple numerical algorithm. We illustrate our proposals using simulated and stock returns data.

Did sovereign default risk affect macroeconomic activity through firms' access to credit during the European sovereign debt crisis? We investigate this question by a estimating a structural panel vector autoregressive model for Italy, Spain, Portugal, and Ireland, where the sovereign risk shock is identified using sign restrictions. The results suggest that decline in the creditworthiness of the sovereign contributed to a fall in private lending and economic activity in several euro-area countries by reducing the value of banks' assets and crowding out private lending.

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We illustrate our findings with applications to risk assessment in financial systems and reinsurance markets under a bipartite network structure.

Improving productivity among farm microenterprises is important, especially in low-income countries where market imperfections are pervasive and resources are scarce. Relaxing credit constraints can increase the productivity of farmers. Using a field experiment involving microenterprises in Bangladesh, we estimate the impact of access to credit on the overall productivity of rice farmers, and disentangle the total effect into technological change (frontier shift) and technical efficiency changes. We find that relative to the baseline rice output per decimal, access to credit results in, on average, approximately a 14 percent increase in yield, holding all other inputs constant. After decomposing the total effect into the frontier shift and efficiency improvement, we find that, on average, around 11 percent of the increase in output comes from changes in technology, or frontier shift, while the remaining 3 percent is attributed to improvements in technical efficiency. The efficiency gain is higher for modern hybrid rice varieties, and almost zero for traditional rice varieties. Within the treatment group, the effect is greater among pure tenant and mixed-tenant farm households compared with farmers that only cultivate their own land.

Numerous studies have considered the important role of cognition in estimating the returns to schooling. How cognitive abilities affect schooling may have important policy implications, especially in developing countries during periods of increasing educational attainment. Using two longitudinal labor surveys that collect direct proxy measures of cognitive skills, we study the importance of specific cognitive domains for the returns to schooling in two samples. We instrument for schooling levels and we find that each additional year of schooling leads to an increase in earnings by approximately 18-20 percent. The estimated effect sizes-based on the two-stage least squares estimates-are above the corresponding ordinary least squares estimates. Furthermore, we estimate and demonstrate the importance of specific cognitive domains in the classical Mincer equation. We find that executive functioning skills (i.e., memory and orientation) are important drivers of earnings in the rural sample, whereas higher-order cognitive skills (i.e., numeracy) are more important for determining earnings in the urban sample. Although numeracy is tested in both samples, it is only a statistically significant predictor of earnings in the urban sample.

Continuous stochastic processes are widely used to model time series that exhibit a random behaviour. Predictions of the stochastic process can be computed by the conditional expectation given the current information. To this end, we introduce the controlled ODE-RNN that provides a data-driven approach to learn the conditional expectation of a stochastic process. Our approach extends the ODE-RNN framework which models the latent state of a recurrent neural network (RNN) between two observations with a neural ordinary differential equation (neural ODE). We show that controlled ODEs provide a general framework which can in particular describe the ODE-RNN, combining in a single equation the continuous neural ODE part with the jumps introduced by RNN. We demonstrate the predictive capabilities of this model by proving that, under some regularities assumptions, the output process converges to the conditional expectation process.

Against the background of renewed interest in vertical support policies targeting specific industries or technologies, we investigate the effects of vertical vs. horizontal policies in a combinatorial model of economic development. In the framework we propose, an economy develops by acquiring new capabilities allowing for the production of an ever greater variety of products with an increasing complexity. Innovation policy can aim to expand the number of capabilities (vertical policy) or the ability to combine capabilities (horizontal policy). The model shows that for low-income countries, the two policies are complementary. For high-income countries that are specialised in the most complex products, focusing on horizontal policy only yields the highest returns. We reflect on the model results in the light of the contemporary debate on vertical policy.

Evidence on educational returns and the factors that determine the demand for schooling in developing countries is extremely scarce. Building on previous studies that show individuals underestimating the returns to schooling, we use two surveys from Tanzania to estimate both the actual and perceived schooling returns and subsequently examine what factors drive individual misperceptions regarding actual returns. Using ordinary least squares and instrumental variable methods, we find that each additional year of schooling in Tanzania increases earnings, on average, by 9 to 11 percent. We find that on average individuals underestimate returns to schooling by 74 to 79 percent and three factors are associated with these misperceptions: income, asset poverty and educational attainment. Shedding light on what factors relate to individual beliefs about educational returns can inform policy on how to structure effective interventions in order to correct individual misperceptions.