The existing approaches to sparse wealth allocations (1) are suboptimal due to the bias induced by $\ell_1$-penalty; (2) require the number of assets to be less than the sample size; (3) do not model factor structure of stock returns in high dimensions. We address these shortcomings and develop a novel strategy which produces unbiased and consistent sparse allocations. We demonstrate that: (1) failing to correct for the bias leads to low out-of-sample portfolio return; (2) only sparse portfolios achieved positive cumulative return during several economic downturns, including the dot-com bubble of 2000, the financial crisis of 2007-09, and COVID-19 outbreak.

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and L\'evy-driven Ornstein-Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang [23] because it does not rely on an acceptance-rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques

Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American and barrier option pricing in the subdiffusive Black-Scholes model. Two computational methods for valuing American options in the considered model are proposed. The weighted scheme of the finite difference (FD) method is derived and the main properties of the method are presented. The Longstaff-Schwartz method is applied for the discussed model and is compared to the previous method. In the article it is also shown how to valuate numerically wide range of barrier options using the FD approach. The proposed FD method has $2-\alpha$ order of accuracy with respect to time, where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space.

Stock classification is a challenging task due to high levels of noise and volatility of stocks returns. In this paper we show that using transfer learning can help with this task, by pre-training a model to extract universal features on the full universe of stocks of the S$\&$P500 index and then transferring it to another model to directly learn a trading rule. Transferred models present more than double the risk-adjusted returns than their counterparts trained from zero. In addition, we propose the use of data augmentation on the feature space defined as the output of a pre-trained model (i.e. augmenting the aggregated time-series representation). We compare this augmentation approach with the standard one, i.e. augmenting the time-series in the input space. We show that augmentation methods on the feature space leads to $20\%$ increase in risk-adjusted return compared to a model trained with transfer learning but without augmentation.

Motivated by recent applications of sequential decision making in matching markets, in this paper we attempt at formulating and abstracting market designs in peer lending. In the rest of this paper, what will follow is a paradigm to set the stage for how peer lending can be conceived from a matching market perspective with sequential design making embedded in it. We attempt at laying the stepping stones toward understanding how sequential decision making can be made more flexible in peer lending platforms and as a way to devise more fair and equitable outcomes for both borrowers and lenders. The goal of this paper is to provide some ideas on how and why lending platforms conceived from the perspective of matching markets can allow for incorporating fairness and equitable outcomes when we design lending platforms.

In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, $(X,Y,T)$, where $X$ and $Y$ are independent Brownian motions. We show the equivalent conditions for the triplet being independent. We discuss the connection and difference of the common decomposition with the local correlation model. Indicated by the discussion, we propose a new method for constructing correlated Brownian motions which performs very well in simulation. For applications, we use these very general results for pricing two-factor financial derivatives whose payoffs rely very much on the correlations of underlyings. And in addition, with the help of numerical method, we also make a discussion of the pricing deviation when substituting a constant correlation model for a general one.

We consider shared listings on two South African equity exchanges: the Johannesburg Stock Exchange (JSE) and the A2X Exchange. A2X is an alternative exchange that provides for both shared listings and new listings within the financial market ecosystem of South Africa. From a science perspective it provides the opportunity to compare markets trading similar shares, in a similar regulatory and economic environment, but with vastly different liquidity, costs and business models. A2X currently has competitive settlement and transaction pricing when compared to the JSE, but the JSE has deeper liquidity. In pursuit of an empirical understanding of how these differences relate to their respective price response dynamics, we compare the distributions and auto-correlations of returns on different time scales; we compare price impact and master curves; and we compare the cost of trading on each exchange. This allows us to empirically compare the two markets. We find that various stylised facts become similar as the measurement or sampling time scale increase. However, the same securities can have vastly different price responses irrespective of time scales. This is not surprising given the different liquidity and order-book resilience. Here we demonstrate that direct costs dominate the cost of trading, and the importance of competitively positioning cost ceilings. Universality is crucial for being able to meaningfully compare cross-exchange price responses, but in the case of A2X, it has yet to emerge in a meaningful way due to the infancy of the exchange -- making meaningful comparisons difficult.

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard game-theoretic formulations of this problem assume that agents act in accordance with a specific behavioral model. In practice, however, some agents may not prescribe to the dominant behavioral model or may act in ways that are seemingly arbitrarily irrational. Existing algorithms heavily depend on the behavioral model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrarily irrational agents.

We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying behavioral model. In particular, we provide two algorithms, one built on robustifying multidimensional binary search methods and one on translating the setting to a proxy setting appropriate for gradient descent. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.

Deep reinforcement learning (DRL) has reached super human levels in complex tasks like game solving (Go and autonomous driving). However, it remains an open question whether DRL can reach human level in applications to financial problems and in particular in detecting pattern crisis and consequently dis-investing. In this paper, we present an innovative DRL framework consisting in two sub-networks fed respectively with portfolio strategies past performances and standard deviations as well as additional contextual features. The second sub network plays an important role as it captures dependencies with common financial indicators features like risk aversion, economic surprise index and correlations between assets that allows taking into account context based information. We compare different network architectures either using layers of convolutions to reduce network's complexity or LSTM block to capture time dependency and whether previous allocations is important in the modeling. We also use adversarial training to make the final model more robust. Results on test set show this approach substantially over-performs traditional portfolio optimization methods like Markowitz and is able to detect and anticipate crisis like the current Covid one.

This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. Dynamic sensitivities are then used to compute Dynamic Initial Margin as defined by ISDA (SIMM). The technique is benchmarked against the computation of dynamic sensitivities obtained by using pricing functions like the ones found in risk engines. We obtain high accuracy and computational gains for FX swaps and Spread Options.

The structures, including technologies, industries, infrastructure and institutions, in a country have three attributes, namely, structurality, durationality, and transformality. The paper proposes a novel method to model the structural transformation in a market economy. With the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structure and the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's utility in a market economy. The paper establishes the mathematical underpinning of the static equilibrium, dynamic equilibrium and structural equilibrium. The generic model and its equilibria are then extended to economies with complicated economic structures consisting of hierarchical production, composite consumption, technology adoption and innovation, infrastructure, and economic and political institutions. The paper concludes with a brief discussion of applications of the proposed methodology to economic development problems in other scenarios.

In this paper, we consider a variety of multi-state Hidden Markov models for predicting and explaining the Bitcoin, Ether and Ripple returns in the presence of state (regime) dynamics. In addition, we examine the effects of several financial, economic and cryptocurrency specific predictors on the cryptocurrency return series. Our results indicate that the 4-states Non-Homogeneous Hidden Markov model has the best one-step-ahead forecasting performance among all the competing models for all three series. The superiority of the predictive densities, over the single regime random walk model, relies on the fact that the states capture alternating periods with distinct returns' characteristics. In particular, we identify bull, bear and calm regimes for the Bitcoin series, and periods with different profit and risk magnitudes for the Ether and Ripple series. Finally, we observe that conditionally on the hidden states, the predictors have different linear and non-linear effects.

This paper identifies latent group structures in the effect of motherhood on employment by employing the C-Lasso, a recently developed, purely data-driven classification method. Moreover, I assess how the introduction of the generous German parental benefit reform in 2007 affects the different cluster groups by taking advantage of an identification strategy that combines the sharp regression discontinuity design and hypothesis testing of predicted employment probabilities. The C-Lasso approach enables heterogeneous employment effects across mothers, which are classified into an a priori unknown number of cluster groups, each with its own group-specific effect. Using novel German administrative data, the C-Lasso identifies three different cluster groups pre- and post-reform. My findings reveal marked unobserved heterogeneity in maternal employment and that the reform affects the identified cluster groups' employment patterns differently.

We present a baseline stochastic framework for assessing inter-sectorial relationships in a generic economy. We show that - irrespective of the specific features of the technology matrix for a given country or a particular year - the Leontief multipliers (and any upstreamness/downstreamness indicator computed from the Leontief inverse matrix) follow a universal pattern, which we characterize analytically. We formulate a universal benchmark to assess the structural inter-dependence of sectors in a generic economy. Several empirical results on World Input-Output Database (WIOD, 2013 Release) are presented that corroborate our findings.

We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related to the market index factor and to the conditional correlations between stocks. Those interpretations lead to a set of guidelines that users should be aware of when estimating graphs in financial markets. In addition, we propose algorithms to learn undirected graphs that account for stylized facts and tasks intrinsic to financial data such as non-stationarity and stock clustering.

This paper presents a tractable model of non-linear dynamics of market returns using a Langevin approach.Due to non-linearity of an interaction potential, the model admits regimes of both small and large return fluctuations. Langevin dynamics are mapped onto an equivalent quantum mechanical (QM) system. Borrowing ideas from supersymmetric quantum mechanics (SUSY QM), we use a parameterized ground state wave function (WF) of this QM system as a direct input to the model, which also fixes a non-linear Langevin potential. A stationary distribution of the original Langevin model is given by the square of this WF, and thus is also a direct input to the model. Using a two-component Gaussian mixture as a ground state WF with an asymmetric double well potential produces a tractable low-parametric model with interpretable parameters, referred to as the NES (Non-Equilibrium Skew) model. Supersymmetry (SUSY) is then used to find time-dependent solutions of the model in an analytically tractable way. The model produces time-varying variance, skewness and kurtosis of market returns, whose time variability can be linked to probabilities of crisis-like events. For option pricing out of equilibrium, the NES model offers a closed-form approximation by a mixture of three Black-Scholes prices, which can be calibrated to index options data and used to predict moments of future returns. The NES model is shown to be able to describe both regimes of a benign market and a market in a crisis or a severe distress.

In this study we arrive at a closed form expression for measuring vector assortativity in networks motivated by our use-case which is to observe patterns of social mobility in a society. Based on existing works on social mobility within economics literature, and social reproduction within sociology literature, we motivate the construction of an occupational network structure to observe mobility patterns. Basing on existing literature, over this structure, we define mobility as assortativity of occupations attributed by the representation of categories such as gender, geography or social groups. We compare the results from our vector assortativity measure and averaged scalar assortativity in the Indian context, relying on NSSO 68th round on employment and unemployment. Our findings indicate that the trends indicated by our vector assortativity measure is very similar to what is indicated by the averaged scalar assortativity index. We discuss some implications of this work and suggest future directions.

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 studies politically feasible policy solutions to inequities in local public goods provision. I focus in particular on the entwined issues of high property taxes, geographic income disparities, and inequalities in public education prevalent in the United States. It has long been recognized that with a mobile population, local administration and funding of schools leads to competition between districts. By accounting for heterogeneity in incomes and home qualities, I am able to shed new light on this phenomenon, and make novel policy recommendations. I characterize the equilibrium in a dynamic general equilibrium model of location choice and education investment with a competitive housing market, heterogeneous wealth levels and home qualities, and strategic district governments. When all homes are owner-occupied, I show that competition between strategic districts leads to over-taxation in an attempt to attract wealthier residents. A simple class of policies that cap and/or tax the expenditure of richer districts are Pareto improving, and thus politically feasible. These policies reduce inequality in access to education while increasing expenditure for under-funded schools. Gains are driven by mitigation of the negative externalities generated by excessive spending among wealthier districts. I also discuss the policy implications of the degree of homeownership. The model sheds new light on observed patterns of homeownership, location choice, and income. Finally, I test the assumptions and implications empirically using a regression discontinuity design and data on property tax referenda in Massachusetts.

Inspired by the developments in deep generative models, we propose a model-based RL approach, coined Reinforced Deep Markov Model (RDMM), designed to integrate desirable properties of a reinforcement learning algorithm acting as an automatic trading system. The network architecture allows for the possibility that market dynamics are partially visible and are potentially modified by the agent's actions. The RDMM filters incomplete and noisy data, to create better-behaved input data for RL planning. The policy search optimisation also properly accounts for state uncertainty. Due to the complexity of the RKDF model architecture, we performed ablation studies to understand the contributions of individual components of the approach better. To test the financial performance of the RDMM we implement policies using variants of Q-Learning, DynaQ-ARIMA and DynaQ-LSTM algorithms. The experiments show that the RDMM is data-efficient and provides financial gains compared to the benchmarks in the optimal execution problem. The performance improvement becomes more pronounced when price dynamics are more complex, and this has been demonstrated using real data sets from the limit order book of Facebook, Intel, Vodafone and Microsoft.

The electricity market, which was initially designed for dispatchable power plants and inflexible demand, is being increasingly challenged by new trends, such as the high penetration of intermittent renewables and the transformation of the consumers energy space. To accommodate these new trends and improve the performance of the market, several modifications to current market designs have been proposed in the literature. Given the vast variety of these proposals, this paper provides a comprehensive investigation of the modifications proposed in the literature as well as a detailed assessment of their suitability for improving market performance under the continuously evolving electricity landscape. To this end, first, a set of criteria for an ideal market design is proposed, and the barriers present in current market designs hindering the fulfillment of these criteria are identified. Then, the different market solutions proposed in the literature, which could potentially mitigate these barriers, are extensively explored. Finally, a taxonomy of the proposed solutions is presented, highlighting the barriers addressed by each proposal and the associated implementation challenges. The outcomes of this analysis show that even though each barrier is addressed by at least one proposed solution, no single proposal is able to address all the barriers simultaneously. In this regard, a future-proof market design must combine different elements of proposed solutions to comprehensively mitigate market barriers and overcome the identified implementation challenges. Thus, by thoroughly reviewing this rich body of literature, this paper introduces key contributions enabling the advancement of the state-of-the-art towards increasingly efficient electricity market.

This work proposes a supervised multi-channel time-series learning framework for financial stock trading. Although many deep learning models have recently been proposed in this domain, most of them treat the stock trading time-series data as 2-D image data, whereas its true nature is 1-D time-series data. Since the stock trading systems are multi-channel data, many existing techniques treating them as 1-D time-series data are not suggestive of any technique to effectively fusion the information carried by the multiple channels. To contribute towards both of these shortcomings, we propose an end-to-end supervised learning framework inspired by the previously established (unsupervised) convolution transform learning framework. Our approach consists of processing the data channels through separate 1-D convolution layers, then fusing the outputs with a series of fully-connected layers, and finally applying a softmax classification layer. The peculiarity of our framework - SuperDeConFuse (SDCF), is that we remove the nonlinear activation located between the multi-channel convolution layers and the fully-connected layers, as well as the one located between the latter and the output layer. We compensate for this removal by introducing a suitable regularization on the aforementioned layer outputs and filters during the training phase. Specifically, we apply a logarithm determinant regularization on the layer filters to break symmetry and force diversity in the learnt transforms, whereas we enforce the non-negativity constraint on the layer outputs to mitigate the issue of dead neurons. This results in the effective learning of a richer set of features and filters with respect to a standard convolutional neural network. Numerical experiments confirm that the proposed model yields considerably better results than state-of-the-art deep learning techniques for real-world problem of stock trading.

As more tech companies engage in rigorous economic analyses, we are confronted with a data problem: in-house papers cannot be replicated due to use of sensitive, proprietary, or private data. Readers are left to assume that the obscured true data (e.g., internal Google information) indeed produced the results given, or they must seek out comparable public-facing data (e.g., Google Trends) that yield similar results. One way to ameliorate this reproducibility issue is to have researchers release synthetic datasets based on their true data; this allows external parties to replicate an internal researcher's methodology. In this brief overview, we explore synthetic data generation at a high level for economic analyses.

This study introduces a new technique to recover the implicit discount factor in the derivative market using only European put and call prices: this discount is grounded in actual transactions in active markets. Moreover, this study identifies the implied cost of funding, over OIS, of major market players. Does a liquid equity market allow arbitrage? The key idea is that the (unique) forward contract -- built using the put-call parity relation -- contains information about the market discount factor: by no-arbitrage conditions we identify the implicit interest rate such that the forward contract value does not depend on the strike. The procedure is applied to options on S&P 500 and EURO STOXX 50 indices. There is statistical evidence that, in the EURO STOXX 50 market, the implicit interest rate curve coincides with the EUR OIS one, while, in the S&P 500 market, a cost of funding of, on average, 34 basis points is added on top of the USD OIS curve.

Can an asset manager plan the optimal timing for her/his hedging strategies given market conditions? The standard approach based on Markowitz or other more or less sophisticated financial rules aims to find the best portfolio allocation thanks to forecasted expected returns and risk but fails to fully relate market conditions to hedging strategies decision. In contrast, Deep Reinforcement Learning (DRL) can tackle this challenge by creating a dynamic dependency between market information and hedging strategies allocation decisions. In this paper, we present a realistic and augmented DRL framework that: (i) uses additional contextual information to decide an action, (ii) has a one period lag between observations and actions to account for one day lag turnover of common asset managers to rebalance their hedge, (iii) is fully tested in terms of stability and robustness thanks to a repetitive train test method called anchored walk forward training, similar in spirit to k fold cross validation for time series and (iv) allows managing leverage of our hedging strategy. Our experiment for an augmented asset manager interested in sizing and timing his hedges shows that our approach achieves superior returns and lower risk.

The purpose of this paper is to test the multi-factor beta model implied by the generalized arbitrage pricing theory (APT) and the Adaptive Multi-Factor (AMF) model with the Groupwise Interpretable Basis Selection (GIBS) algorithm, without imposing the exogenous assumption of constant betas. The intercept (arbitrage) tests validate both the AMF and the Fama-French 5-factor (FF5) model. We do the time-invariance tests for the betas for both the AMF model and the FF5 in various time periods. We show that for nearly all time periods with length less than 6 years, the beta coefficients are time-invariant for the AMF model, but not the FF5 model. The beta coefficients are time-varying for both AMF and FF5 models for longer time periods. Therefore, using the dynamic AMF model with a decent rolling window (such as 5 years) is more powerful and stable than the FF5 model.

In this paper we introduce a new concept for modelling electricity prices through the introduction of an unobservable intrinsic electricity price $p(\tau)$. We use it to connect the classical theory of storage with the concept of a risk premium. We derive prices for all common contracts such as the intraday spot price, the day-ahead spot price, and futures prices. Finally, we propose an explicit model from the class of structural models and conduct an empirical analysis, where we find an overall negative risk premium.

We consider a model-independent pricing problem in a fixed-income market and show that it leads to a weak optimal transport problem as introduced by Gozlan et al. We use this to characterize the extremal models for the pricing of caplets on the spot rate and to establish a first robust super-replication result that is applicable to fixed-income markets.

Notably, the weak transport problem exhibits a cost function which is non-convex and thus not covered by the standard assumptions of the theory. In an independent section, we establish that weak transport problems for general costs can be reduced to equivalent problems that do satisfy the convexity assumption, extending the scope of weak transport theory. This part could be of its own interest independent of our financial application, and is accessible to readers who are not familiar with mathematical finance notations.

Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market. In this article, we include a possible crisis by using an alternating renewal process to describe the switching between a normal financial regime and a financial crisis. We develop a framework to price the XVA of a European claim in this state-dependent situation. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of the XVA.