In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated SABR model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss-Hermite quadrature. We further obtain the option price by integrating the CEV option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709-737]. For the uncorrelated SABR model, the new method of option pricing is accurate and arbitrage-free across all strike prices.

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas w.r.t. the estimation of risk measures in risk management.

In this paper, we document a novel machine learning based bottom-up approach for static and dynamic portfolio optimization on, potentially, a large number of assets. The methodology overcomes many major difficulties arising in current optimization schemes. For example, we no longer need to compute the covariance matrix and its inverse for mean-variance optimization, therefore the method is immune from the estimation error on this quantity. Moreover, no explicit calls of optimization routines are needed.

Applications to a bottom-up mean-variance-skewness-kurtosis or CRRA (Constant Relative Risk Aversion) optimization with short-sale portfolio constraints in both simulation and real market (China A-shares and U.S. equity markets) environments are studied and shown to perform very well.

We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical recipes to compute the rate function; the backbone of our theoretical framework. Based on our results, we further develop approximation schemes for the density of RV, which in turn allows to express the volatility swap in close-form. Lastly, we investigate different constructions of multi-factor models and how each of them affects the convexity of the implied volatility smile. Interestingly, we identify the class of models that generate non-linear smiles around-the-money.

This paper examines the dynamic interaction between falling and rising markets for both the real and the financial sectors of the largest economy in the world using asymmetric causality tests. These tests require that each underlying variable in the model be transformed into partial sums of the positive and negative components. The positive components represent the rising markets and the negative components embody the falling markets. The sample period covers some part of the COVID19 pandemic. Since the data is non normal and the volatility is time varying, the bootstrap simulations with leverage adjustments are used in order to create reliable critical values when causality tests are conducted. The results of the asymmetric causality tests disclose that the bear markets are causing the recessions as well as the bull markets are causing the economic expansions. The causal effect of bull markets on economic expansions is higher compared to the causal effect of bear markets on economic recessions. In addition, it is found that economic expansions cause bull markets but recessions do not cause bear markets. Thus, the policies that remedy the falling financial markets can also help the economy when it is in a recession.

Using neural networks, we compute bounds on the prices of multi-asset derivatives given information on prices of related payoffs. As a main example, we focus on European basket options and include information on the prices of other similar options, such as spread options and/or basket options on subindices. We show that, in most cases, adding further constraints gives rise to bounds that are considerably tighter and discuss the maximizing/minimizing copulas achieving such bounds. Our approach follows the literature on constrained optimal transport and, in particular, builds on a recent paper by Eckstein and Kupper (2019, Appl. Math. Optim.).

Campbell-Goodhart's law relates to the causal inference error whereby decision-making agents aim to influence variables which are correlated to their goal objective but do not reliably cause it. This is a well known error in Economics and Political Science but not widely labelled in Artificial Intelligence research. Through a simple example, we show how off-the-shelf deep Reinforcement Learning (RL) algorithms are not necessarily immune to this cognitive error. The off-policy learning method is tricked, whilst the on-policy method is not. The practical implication is that naive application of RL to complex real life problems can result in the same types of policy errors that humans make. Great care should be taken around understanding the causal model that underpins a solution derived from Reinforcement Learning.

In an Ito-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent, existing assumptions -- such as, the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases, thus also extending the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Ito-diffusion markets under the presence of correlated random endowment process for both the perfectly and the incomplete market cases.

We establish a rigorous duality theory for a finite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed time, independent of the asset prices. We thus close a duality gap encountered by Vellekoop and Davis in an infinite horizon version of this problem. Nearly all the classical tenets of duality theory are found to hold, with the notable exception that the marginal utility of initial wealth at zero is finite. The intuition is that the agent will receive some income, no matter how early it terminates, so is not infinitely penalised for having zero initial capital. We then solve the problem numerically, with an additional terminal wealth objective, using deep learning. We transform the problem with randomly terminating income into one that no longer depends on the jump component but has an additional inter-temporal wealth objective. We then numerically solve the second order backward stochastic differential equations (2BSDEs), in both the primal and dual dimensions, to find the optimal control and tight lower and upper bounds for the value function.

In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short rate follows the subdiffusive fractional Black-Scholes model. We obtain the pricing formula for zero-coupon bond in the introduced model and derive the partial differential equation with appropriate boundary conditions for the valuation of equity warrant. Finally, the pricing formula for equity warrant is provided under subdiffusive fractional Brownian motion model of the short rate.

Mobile phone-based gambling has grown wildly popular in Africa. Commentators worry that low ability gamblers will not learn from experience, and may rely on debt to gamble. Using data on financial transactions for over 50 000 Kenyan smartphone users, we find that gamblers do learn from experience. Gamblers are less likely to bet following poor results and more likely to bet following good results. The reaction to positive and negative feedback is of equal magnitude, and is consistent with a model of Bayesian updating. Using an instrumental variables strategy, we find no evidence that increased gambling leads to increased debt.

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics due to irregularities found when comparing its properties with empirical distributions. As a solution, we develop a generalisation of GBM where the introduction of a memory kernel critically determines the behavior of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and obtain the corresponding probability density functions by using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.

Using machine learning methods in a quasi-experimental setting, I study the heterogeneous effects of introducing waste prices---unit prices on household unsorted waste disposal---on waste demands and social welfare. First, using a unique panel of Italian municipalities with large variation in prices and observables, I show that waste demands are nonlinear. I find evidence of nudge effects at low prices, and increasing elasticities at high prices driven by income effects and waste habits before policy. Second, I estimate policy impacts on pollution and municipal management costs, and compute the overall social cost savings for each municipality. Social welfare effects become positive for most municipalities after three years of adoption, when waste prices cause significant waste avoidance.

The COVID-19 pandemic constitutes one of the largest threats in recent decades to the health and economic welfare of populations globally. In this paper, we analyze different types of policy measures designed to fight the spread of the virus and minimize economic losses. Our analysis builds on a multi-group SEIR model, which extends the multi-group SIR model introduced by Acemoglu et al.~(2020). We adjust the underlying social interaction patterns and consider an extended set of policy measures. The model is calibrated for Germany. Despite the trade-off between COVID-19 prevention and economic activity that is inherent to shielding policies, our results show that efficiency gains can be achieved by targeting such policies towards different age groups. Alternative policies such as physical distancing can be employed to reduce the degree of targeting and the intensity and duration of shielding. Our results show that a comprehensive approach that combines multiple policy measures simultaneously can effectively mitigate population mortality and economic harm.

We show that the problem of existence of equilibrium in Kyle's continuous time insider trading model ([31]) can be tackled by considering a system of quasilinear parabolic equation and a Fokker-Planck equation coupled via a transport type constraint. By obtaining a stochastic representation for the solution of such a system, we show the well-posedness of solutions and study the properties of the equilibrium obtained for small enough risk aversion parameter. In our model, the insider has exponential type utility and the belief of the market on the distribution of the price at final time can be non-Gaussian.

Savage (1972) lays down the foundation of Bayesian decision theory, but asserts that it is not applicable in big worlds where the environment is complex. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in small and big worlds, where the complexity of the environment is low and high, respectively, relative to the cognitive ability of the decision maker. Confirming Savage's claim, optimal learning behavior is closed to Bayesian in small worlds but significantly different in big worlds. In addition, I show that in big worlds, the optimal learning behavior could exhibit a wide range of well-documented non-Bayesian learning behavior, including the use of heuristic, correlation neglect, persistent over-confidence, inattentive learning, and other behaviors of model simplification or misspecification. These results establish a clear and testable relationship between the prominence of non-Bayesian learning behavior, complexity and cognitive ability.

It is argued that Marxism, being based on contradictions, is an illogical method. More specifically, we present a rejection of Marx's thesis that the rate of profit has a long-term tendency to fall.

In this paper, I present a visual representation of the relationship between mean hourly total compensation divided by per-capita GDP, hours worked per capita, and the labor share, and show the represented labor equilibrium equation is the definition of the labor share. I also present visual examination of the productivity horizon and wage compression, and use these to show the relationship between productivity, available employment per capita, and minimum wage. From this I argue that wages are measured in relation to per-capita GDP, and that minimum wage controls income inequality and productivity growth.

We show that the barrier function in Root's solution to the Skorokhod embedding problem is continuous and finite at every point where the target measure has no atom and its absolutely continuous part is locally bounded away from zero.

Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when the stock returns are driven by the common factors, this assumption does not hold. Our paper develops a framework for estimating a high-dimensional precision matrix which combines the benefits of exploring the factor structure of the stock returns and the sparsity of the precision matrix of the factor-adjusted returns. The proposed algorithm is called Factor Graphical Lasso (FGL). We study a high-dimensional portfolio allocation problem when the asset returns admit the approximate factor model. In high dimensions, when the number of assets is large relative to the sample size, the sample covariance matrix of the excess returns is subject to the large estimation uncertainty, which leads to unstable solutions for portfolio weights. To resolve this issue, we consider the decomposition of low-rank and sparse components. This strategy allows us to consistently estimate the optimal portfolio in high dimensions, even when the covariance matrix is ill-behaved. We establish consistency of the portfolio weights in a high-dimensional setting without assuming sparsity on the covariance or precision matrix of stock returns. Our theoretical results and simulations demonstrate that FGL is robust to heavy-tailed distributions, which makes our method suitable for financial applications. The empirical application uses daily and monthly data for the constituents of the S&P500 to demonstrate superior performance of FGL compared to the equal-weighted portfolio, index and some prominent precision and covariance-based estimators.

This paper documents the representation of women in Economics academia in India by analyzing the share of women in faculty positions, and their participation in a prestigious conference held annually. Data from the elite institutions shows that the presence of women as the Economics faculty members remains low. Of the authors of the papers which were in the final schedule of the prestigious research conference, the proportion of women authors is again found to be disproportionately low. Our findings from further analysis indicate that women are not under-represented at the post-graduate level. Further, the proportion of women in doctoral programmes has increased over time, and is now almost proportionate. Tendency of women who earn a doctorate abroad, to not return to India, time needed to complete a doctoral program, and responsibilities towards the family may explain lower presence of women in Economics academia in India.

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from Pontryagin's stochastic maximum principle. Although the same cost functions as well as the coefficient functions of the state dynamics are shared among the agents within each population, they can be different population by population. We study the mean field limit for the three different situations; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative but those in the other populations are not. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each of these cases. Furthermore, under appropriate conditions, we show that the mean field solution to each of these problems actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.

Equal access to voting is a core feature of democratic government. Using data from millions of smartphone users, we quantify a racial disparity in voting wait times across a nationwide sample of polling places during the 2016 U.S. presidential election. Relative to entirely-white neighborhoods, residents of entirely-black neighborhoods waited 29% longer to vote and were 74% more likely to spend more than 30 minutes at their polling place. This disparity holds when comparing predominantly white and black polling places within the same states and counties, and survives numerous robustness and placebo tests. We shed light on the mechanism for these results and discuss how geospatial data can be an effective tool to both measure and monitor these disparities going forward.

Entering the Pandemic Recession, we study the high-frequency real-activity signals provided by a leading nowcast, the ADS Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia. We track the evolution of real-time vintage beliefs and compare them to a later-vintage chronology. Real-time ADS plunges and then swings as its underlying economic indicators swing, but the ADS paths quickly converge to indicate a return to brisk positive growth by mid-May. We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path. Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.

How should central banks optimally aggregate sectoral inflation rates in the presence of imperfect labor mobility across sectors? We study this issue in a two-sector New-Keynesian model and show that a lower degree of sectoral labor mobility, ceteris paribus, increases the optimal weight on inflation in a sector that would otherwise receive a lower weight. We analytically and numerically find that, with limited labor mobility, adjustment to asymmetric shocks cannot fully occur through the reallocation of labor, thus putting more pressure on wages, causing inefficient movements in relative prices, and creating scope for central banks intervention. These findings challenge standard central banks practice of computing sectoral inflation weights based solely on sector size, and unveil a significant role for the degree of sectoral labor mobility to play in the optimal computation. In an extended estimated model of the U.S. economy, featuring customary frictions and shocks, the estimated inflation weights imply a decrease in welfare up to 10 percent relative to the case of optimal weights.

In recent years online social networks have become increasingly prominent in political campaigns and, concurrently, several countries have experienced shock election outcomes. This paper proposes a model that links these two phenomena. In our set-up, the process of learning from others on a network is influenced by confirmation bias, i.e. the tendency to ignore contrary evidence and interpret it as consistent with one's own belief. When agents pay enough attention to themselves, confirmation bias leads to slower learning in any symmetric network, and it increases polarization in society. We identify a subset of agents that become more/less influential with confirmation bias. The socially optimal network structure depends critically on the information available to the social planner. When she cannot observe agents' beliefs, the optimal network is symmetric, vertex-transitive and has no self-loops. We explore the implications of these results for electoral outcomes and media markets. Confirmation bias increases the likelihood of shock elections, and it pushes fringe media to take a more extreme ideology.

The implementation of large-scale containment measures by governments to contain the spread of the COVID-19 virus has resulted in a large supply and demand shock throughout the global economy. Here, we use empirical vessel tracking data and a newly developed algorithm to estimate the global maritime trade losses during the first eight months of the pandemic. Our results show widespread trade losses on a port level with the largest absolute losses found for ports in China, the Middle-East and Western Europe, associated with the collapse of specific supply-chains (e.g. oil, vehicle manufacturing). In total, we estimate that global maritime trade reduced by -7.0% to -9.6% during the first eight months of 2020, which is equal to around 206-286 million tonnes in volume losses and up to 225-412 billion USD in value losses. The fishery, mining and quarrying, electrical equipment and machinery manufacturing, and transport equipment manufacturing sectors are hit hardest, with losses up to 11.8%. Moreover, we find a large geographical disparity in losses, with some small islands developing states and low-income economies suffering the largest relative trade losses. We find a clear negative impact of COVID-19 related business and public transport closures on country-wide exports. Overall, we show how real-time indicators of economic activity can support governments and international organisations in economic recovery efforts and allocate funds to the hardest hit economies and sectors.

Quantile regression is an efficient tool when it comes to estimate popular measures of tail risk such as the conditional quantile Value at Risk. In this paper we exploit the availability of data at mixed frequency to build a volatility model for daily returns with low-- (for macro--variables) and high--frequency (which may include an \virg{--X} term related to realized volatility measures) components. The quality of the suggested quantile regression model, labeled MF--Q--ARCH--X, is assessed in a number of directions: we derive weak stationarity properties, we investigate its finite sample properties by means of a Monte Carlo exercise and we apply it on financial real data. VaR forecast performances are evaluated by backtesting and Model Confidence Set inclusion among competitors, showing that the MF--Q--ARCH--X has a consistently accurate forecasting capability.