With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel portfolio management strategy based on the framework of Deep Deterministic Policy Gradient, a policy-based reinforcement learning framework, and compare its performance to that of other trading strategies. In our framework, two Long Short-Term Memory neural networks and two fully connected neural networks are constructed. We also investigate the performance of our strategy with and without transaction costs. Experimentally, we choose eight US stocks consisting of four low-volatility stocks and four high-volatility stocks. We compare the compound annual return rate of our strategy against seven other strategies, e.g., Uniform Buy and Hold, Exponential Gradient and Universal Portfolios. In our case, the compound annual return rate is 14.12%, outperforming all other strategies. Furthermore, in terms of Sharpe Ratio (0.5988), our strategy is nearly 33% higher than that of the second-best performing strategy.

We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the determination of optimal hedging strategies attaining these bounds. In particular, our methodology allows to train a single neural network offline and then to use it online for the fast determination of model-free price bounds of a whole class of financial derivatives with current market data. We show the applicability of this approach and highlight its accuracy in several examples involving real market data. Further, we show how a neural network can be trained to solve martingale optimal transport problems involving fixed marginal distributions instead of financial market data.

The growth in AI is rapidly transforming the structure of economic production. However, very little is known about how within-AI specialization may relate to broad-based economic diversification. This paper provides a data-driven framework to integrate the interconnection between AI-based specialization with goods and services export specialization to help design future comparative advantage based on the inherent capabilities of nations. Using detailed data on private investment in AI and export specialization for more than 80 countries, we propose a systematic framework to help identify the connection from AI to goods and service sector specialization. The results are instructive for nations that aim to harness AI specialization to help guide sources of future competitive advantage. The operational framework could help inform the public and private sector to uncover connections with nearby areas of specialization.

We price American options using kernel-based approximations of the Volterra Heston model. We choose these approximations because they allow simulation-based techniques for pricing. We prove the convergence of American option prices in the approximating sequence of models towards the prices in the Volterra Heston model. A crucial step in the proof is to exploit the affine structure of the model in order to establish explicit formulas and convergence results for the conditional Fourier-Laplace transform of the log price and an adjusted version of the forward variance. We illustrate with numerical examples our convergence result and the behavior of American option prices with respect to certain parameters of the model.

In this paper, we use rich administrative data to study a market system for annuity contracts in Chile. To this end, we develop a model of demand and supply of annuities using discrete choice and multi-attribute auctions where life insurance companies with different risk ratings and private information about their annuitization costs compete for savings of risk-averse retirees by offering them personalized pensions. We find that (1) retirees' preferences for firms' risk ratings decrease with their savings, (2) almost half of the retirees who choose annuities do not value bequests, (3) information processing costs are larger for low savers and for those who receive advise from sales-agent, and (4) firms are more likely to have lower annuitization costs for the top 40% savers. Counterfactuals suggest that information asymmetry hurts these 40% savers the most, and replacing the current mechanism with standard English auctions and "shutting-down" risk ratings increase pensions for everyone. But the increase is negligible for most, except for these top 40% savers, with little effect on welfare.

The portfolios are a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of risk statistics from the perspective of time value of the money. This new risk statistic can be uesd for the quantification of portfolio risk. By further developing the properties related to cash sub-additive risk statistics, we are able to derive representation results for such risk.

Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently proposed machine learning algorithm, deep fictitious play, provides a novel efficient tool for finding Markovian Nash equilibrium of large $N$-player asymmetric stochastic differential games [J. Han and R. Hu, Mathematical and Scientific Machine Learning Conference, pages 221-245, PMLR, 2020]. By incorporating the idea of fictitious play, the algorithm decouples the game into $N$ sub-optimization problems, and identifies each player's optimal strategy with the deep backward stochastic differential equation (BSDE) method parallelly and repeatedly. In this paper, we prove the convergence of deep fictitious play (DFP) to the true Nash equilibrium. We can also show that the strategy based on DFP forms an $\eps$-Nash equilibrium. We generalize the algorithm by proposing a new approach to decouple the games, and present numerical results of large population games showing the empirical convergence of the algorithm beyond the technical assumptions in the theorems.

Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based risk measures, we establish new analytical bounds for quantile aggregation which we call convolution bounds. In fact, convolution bounds unify every analytical result and contribute more to the theory of quantile aggregation, and thus these bounds are genuinely the best one available. Moreover, convolution bounds are easy to compute, and we show that they are sharp in many relevant cases. Convolution bounds enjoy several other advantages, including interpretability on the extremal dependence structure, tractability, and theoretical properties. The results directly lead to bounds on the distribution of the sum of random variables with arbitrary dependence, and we illustrate a few applications in operations research.

We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be used to implement a stochastic implied volatility model in the following two steps: 1. Train a market simulator for option prices, as discussed for example in our recent; 2. Find a risk-neutral density, specifically the minimal entropy martingale measure. The resulting model can be used for risk-neutral pricing, or for Deep Hedging in the case of transaction costs or trading constraints. To motivate the proposed approach, we also show that market dynamics are free from "statistical arbitrage" in the absence of transaction costs if and only if they follow a risk-neutral measure. We additionally provide a more general characterization in the presence of convex transaction costs and trading constraints. These results can be seen as an analogue of the fundamental theorem of asset pricing for statistical arbitrage under trading frictions and are of independent interest.

Previous research on two-dimensional extensions of Hotelling's location game has argued that spatial competition leads to maximum differentiation in one dimensions and minimum differentiation in the other dimension. We expand on existing models to allow for endogenous entry into the market. We find that competition may lead to the min/max finding of previous work but also may lead to maximum differentiation in both dimensions. The critical issue in determining the degree of differentiation is if existing firms are seeking to deter entry of a new firm or to maximizing profits within an existing, stable market.

The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use the historical record of futures prices to construct dynamic arbitrage-free models for the SOFR term structure. The models allow you to construct forward-looking SOFR term rates, imply a SOFR discounting curve and price and risk and risk manage SOFR derivatives, not yet liquidly traded in the market. We find that a standard three-factor Gaussian arbitrage-free Nelson-Siegel model describes term rates very well but a shadow-rate extension is needed to describe the behaviour near the zero-boundary. We also find that the jumps and seasonal effects observed in SOFR, do not need to be specifically accounted for in a model for the futures prices. Finally we study the so-called convexity correction and find that it becomes significant beyond the 2 year maturity. For validation purposes we demonstrate that our model aligns closely with the methodology used by the Federal Reserve to publish indicative SOFR term rates.

To address complex problems, scholars are increasingly faced with challenges of integrating diverse knowledge domains. We analyzed the evolution of this convergence paradigm in the broad ecosystem of brain science, which provides a real-time testbed for evaluating two modes of cross-domain integration - subject area exploration via expansive learning and cross-disciplinary collaboration among domain experts. We show that research involving both modes features a 16% citation premium relative to a mono-disciplinary baseline. Further comparison of research integrating neighboring versus distant research domains shows that the cross-disciplinary mode is essential for integrating across relatively large disciplinary distances. Yet we find research utilizing cross-domain subject area exploration alone - a convergence shortcut - to be growing in prevalence at roughly 3% per year, significantly faster than the alternative cross-disciplinary mode, despite being less effective at integrating domains and markedly less impactful. By measuring shifts in the prevalence and impact of different convergence modes in the 5-year intervals before and after 2013, our results indicate that these counterproductive patterns may relate to competitive pressures associated with global Human Brain flagship funding initiatives. Without additional policy guidance, such Grand Challenge flagships may unintentionally incentivize such convergence shortcuts, thereby undercutting the advantages of cross-disciplinary teams in tackling challenges calling on convergence.

Most existing studies on the double/debiased machine learning method concentrate on the causal parameter estimation recovering from the first-order orthogonal score function. In this paper, we will construct the $k^{\mathrm{th}}$-order orthogonal score function for estimating the average treatment effect (ATE) and present an algorithm that enables us to obtain the debiased estimator recovered from the score function. Such a higher-order orthogonal estimator is more robust to the misspecification of the propensity score than the first-order one does. Besides, it has the merit of being applicable with many machine learning methodologies such as Lasso, Random Forests, Neural Nets, etc. We also undergo comprehensive experiments to test the power of the estimator we construct from the score function using both the simulated datasets and the real datasets.

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.

A vastly growing literature on explaining deep learning models has emerged. This paper contributes to that literature by introducing a global gradient-based model-agnostic method, which we call Marginal Attribution by Conditioning on Quantiles (MACQ). Our approach is based on analyzing the marginal attribution of predictions (outputs) to individual features (inputs). Specificalllly, we consider variable importance by mixing (global) output levels and, thus, explain how features marginally contribute across different regions of the prediction space. Hence, MACQ can be seen as a marginal attribution counterpart to approaches such as accumulated local effects (ALE), which study the sensitivities of outputs by perturbing inputs. Furthermore, MACQ allows us to separate marginal attribution of individual features from interaction effect, and visually illustrate the 3-way relationship between marginal attribution, output level, and feature value.

In this paper we consider the strategic asset allocation of an insurance company. This task can be seen as a special case of portfolio optimization. In the 1950s, Markowitz proposed to formulate portfolio optimization as a bicriteria optimization problem considering risk and return as objectives. However, recent developments in the field of insurance require four and more objectives to be considered, among them the so-called solvency ratio that stems from the Solvency II directive of the European Union issued in 2009. Moreover, the distance to the current portfolio plays an important role. While literature on portfolio optimization with three objectives is already scarce, applications with four and more objectives have not yet been solved so far by multi-objective approaches based on scalarizations. However, recent algorithmic improvements in the field of exact multi-objective methods allow the incorporation of many objectives and the generation of well-spread representations within few iterations. We describe the implementation of such an algorithm for a strategic asset allocation with four objective functions and demonstrate its usefulness for the practitioner. Our approach is in operative use in a German insurance company. Our partners report a significant improvement in their decision making process since, due to the proper integration of the new objectives, the software proposes portfolios of much better quality than before within short running time.

This paper proposes two kinds of time-inconsistent preferences (i.e. time flow inconsistency and critical time point inconsistency) to further advance the research on the exit decision of venture capital. Time-inconsistent preference, different from time-consistent preference, assumes that decision makers prefer recent returns rather than future returns. Based on venture capitalists' understanding of future preferences, we consider four types of venture capitalists, namely time-consistent venture capitalists, venture capitalists who only realize critical time point inconsistency, naive venture capitalists and sophisticated venture capitalists, of which the latter three are time-inconsistent. All types of time-inconsistent venture capitalists are aware of critical time point inconsistency. Naive venture capitalists misunderstand time flow inconsistency while sophisticated ones understand it correctly. We propose an optimal exit timing of venture capital model. Then we derive and compare the above four types of venture capitalists' exit thresholds. The main results are as follows: (1) all types of time-inconsistent venture capitalists tend to exit earlier than time-consistent venture capitalists. (2) The longer the expire date are, the more likely venture capitalists are to delay the exit, but the delay degree decreases successively (venture capitalists who only realize critical time point inconsistency > naive venture capitalists > sophisticated venture capitalists).

Product personalization opens the door to price discrimination. A rich product line allows for higher consumer satisfaction, but the mere choice of a product carries valuable information about the consumer that the firm can leverage for price discrimination. Controlling the degree of product personalization provides the firm with an additional tool to curb ratcheting forces arising from consumers' awareness of being price discriminated. Indeed, a firm's inability to not engage in price discrimination introduces a novel distortion: The firm offers a subset of the products that it would offer if, instead, the firm could commit to not price discriminate. Doing so gives commitment power to the firm: By "pooling" consumers with different tastes to the same variety the firm commits not to learn their tastes.

Growth rate of real GDP per capita, GDPpc, is represented as a sum of two components, a monotonically decreasing economic trend and fluctuations related to population change. The economic trend is modelled by an inverse function of GDPpc with a constant numerator which varies for the largest developed economies. In 2006, a statistical analysis conducted for 19 selected OECD countries for the period between 1950 and 2003 showed a very weak linear trend in the annual GDPpc increment for the largest economies: the USA, Japan, France, Italy, and Spain. The UK, Australia, and Canada showed a slightly steeper positive linear trend. The 2012 revision showed that the positive trends became much lower and some of them fell below zero due to the Great Recession. The fluctuations around the trend values are characterized by a quasi-normal distribution with heavy and asymmetric tails. This research revises the previous estimates and extends the set of studied countries by economies in East Europe, Latin America, BRICS, Africa, and Asia including several positive outliers with extremely fast growth. The change in GDP definitions and measuring procedures with time and economic source is discussed in relation to the statistical significance of the trend estimates and data quality requirements for a consistent economic model. The relative performance of all counties since 1960 is compared according to the predicted total GDPpc growth as a function of the initial value. The performance in the 21st century is analyzed separately as revealing potential and actual shifts in the global economic powers.

In this paper, we address risk aggregation and capital allocation problems in the presence of dependence between risks. The dependence structure is defined by a mixed Bernstein copula which represents a generalization of the well-known Archimedean copulas. Using this new copula, the probability density function and the cumulative distribution function of the aggregate risk are obtained. Then, closed-form expressions for basic risk measures, such as tail value-at-risk(TVaR) and TVaR-based allocations, are derived.

We investigate the sources of variability in agricultural production and their relative importance in the context of weather index insurance for smallholder farmers in India. Using parcel-level panel data, multilevel modeling, and Bayesian methods we measure how large a role seasonal variation in weather plays in explaining yield variance. Seasonal variation in weather accounts for 19-20 percent of total variance in crop yields. Motivated by this result, we derive pricing and payout schedules for actuarially fair index insurance. These calculations shed light on the low uptake rates of index insurance and provide direction for designing more suitable index insurance.

Using elementary arguments, we show how to derive $\mathbf{L}_p$-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which pave the way for its asymptotic analysis using stability results for viscosity solutions. Using tools from Malliavin calculus, we also derive simple sufficient conditions for the regularity of frictionless optimal trading strategies, the second main ingredient for the asymptotic analysis of small transaction costs.

Support vector machine modeling is a new approach in machine learning for classification showing good performance on forecasting problems of small samples and high dimensions. Later, it promoted to Support Vector Regression (SVR) for regression problems. A big challenge for achieving reliable is the choice of appropriate parameters. Here, a novel Golden sine algorithm (GSA) based SVR is proposed for proper selection of the parameters. For comparison, the performance of the proposed algorithm is compared with eleven other meta-heuristic algorithms on some historical stock prices of technological companies from Yahoo Finance website based on Mean Squared Error and Mean Absolute Percent Error. The results demonstrate that the given algorithm is efficient for tuning the parameters and is indeed competitive in terms of accuracy and computing time.

This brief technical note introduces PRZI (Parameterised-Response Zero Intelligence), a new form of zero-intelligence trader intended for use in simulation studies of auction markets. Like Gode & Sunder's classic Zero-Intelligence Constrained (ZIC) trader, PRZI generates quote-prices from a random distribution over some specified domain of discretely-valued allowable quote-prices. Unlike ZIC, which uses a uniform distribution to generate prices, the probability distribution in a PRZI trader is parameterised in such a way that its probability mass function (PMF) is determined by a real-valued control variable s in the range [-1.0, +1.0] that determines the strategy for that trader. When s is zero, a PRZI trader behaves identically to the ZIC strategy, with a flat/rectangular PMF; but when s is close to plus or minus one the PRZI trader's PMF becomes asymptotically maximally skewed to one extreme or the other of the price-range, thereby enabling the PRZI trader to act in the same way as the "Shaver" strategy (SHVR) or the "Giveaway" strategy (GVWY), both of which have recently been demonstrated to be surprisingly dominant over more sophisticated, and supposedly more profitable, trader-strategies that incorporate adaptive mechanisms and machine learning. Depending on the value of s, a PRZI trader will behave either as a ZIC, or as a SHVR, or as a GVWY, or as some hybrid strategy part-way between two of these three previously-reported strategies. The novel smoothly-varying strategy in PRZI has value in giving trader-agents plausibly useful "market impact" responses to imbalances in an auction-market's limit-order-book, and also allows for the study of co-adaptive dynamics in continuous strategy-spaces rather than the discrete spaces that have traditionally been studied in the literature.

When it comes to conversations about funding, the questions of whether the United States should be spending its resources on space-based research often rears its head. Opponents of the idea tend to share the opinion that the resources would be better spent helping citizens on the ground. With an estimated homeless population around 562,000 throughout the country, roughly 39.4 million Americans (12.3% of the population) living below the poverty level, and 63.1 million tons of food waste per year, it's hard to argue that the United States does not have its share of problems that need to be addressed. However, a history of space-based research has proven time and time again to bring forth advances in technology and scientific understanding that benefit humans across the globe and provide crucial protection for life on Earth.

In this paper, we reveal the depreciation mechanism of representative money (banknotes) from the perspective of logistics warehousing costs. Although it has long been the dream of economists to stabilize the buying power of the monetary units, the goal we have honest money always broken since the central bank depreciate the currency without limit. From the point of view of modern logistics, the key functions of money are the store of value and low logistics (circulation and warehouse) cost. Although commodity money (such as gold and silver) has the advantages of a wealth store, its disadvantage is the high logistics cost. In comparison to commodity money, credit currency and digital currency cannot protect wealth from loss over a long period while their logistics costs are negligible. We proved that there is not such honest money from the perspective of logistics costs, which is both the store of value like precious metal and without logistics costs in circulation like digital currency. The reason hidden in the back of the depreciation of banknotes is the black hole of storage charge of the anchor overtime after digitizing commodity money. Accordingly, it is not difficult to infer the inevitable collapse of the Bretton woods system. Therefore, we introduce a brand-new currency named honest devalued stable-coin and built a attenuation model of intrinsic value of the honest money based on the change mechanism of storage cost of anchor assets, like gold, which will lay the theoretical foundation for a stable monetary system.

Elections are crucial for legitimating modern democracies, and giving all candidates the possibility to run a proper electoral campaign is necessary for elections' success in providing such legitimization. Yet, during a pandemic, the risk that electoral campaigns would enhance the spread of the disease exists and is substantive. In this work, we estimate the causal impact of electoral campaigns on the spread of COVID-19. Exploiting plausibly exogenous variation in the schedule of local elections across Italy, we show that the electoral campaign preceding this latter led to a significant worsening of the epidemiological situation related to the disease. Our results strongly highlight the importance of undertaking stringent measures along the entire electoral process to minimize its epidemiological consequences.

While the estimation of risk is an important question in the daily business of banks and insurances, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and negatively impacts backtesting results, especially in small sample cases. In this article we show that the link between estimation bias and backtesting can be traced back to the dual relationship between risk measures and the corresponding performance measures, and discuss this in reference to value-at-risk and expected shortfall frameworks. Motivated by this finding, we propose a new algorithm for bias correction and show how to apply it for generalized Pareto distributions. In particular, we consider value-at-risk and expected shortfall plug-in estimators, and show that the application of our algorithm leads to gain in efficiency when heavy tails exist in the data.

In an infinitely repeated pricing game, pricing algorithms based on artificial intelligence (Q-learning) may consistently learn to charge supra-competitive prices even without communication. Although concerns on algorithmic collusion have arisen, little is known on underlying factors. In this work, we experimentally analyze the dynamics of algorithms with three variants of experience replay. Algorithmic collusion still has roots in human preferences. Randomizing experience yields prices close to the static Bertrand equilibrium and higher prices are easily restored by favoring the latest experience. Moreover, relative performance concerns also stabilize the collusion. Finally, we investigate the scenarios with heterogeneous agents and test robustness on various factors.