Optimal Transport Divergences induced by Scoring Functions ArXiv ID: 2311.12183 “View on arXiv” Authors: Unknown Abstract We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume the family of Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. Specifically, we derive the optimal coupling of the MK divergences induced by functionals including the mean, generalised quantiles, expectiles, and shortfall measures. Furthermore, we show that while any elicitable law-invariant coherent risk measure gives raise to infinitely many MK divergences, the comonotonic coupling is simultaneously optimal. The novel MK divergences, which can be efficiently calculated, open an array of applications in robust stochastic optimisation. We derive sharp bounds on distortion risk measures under a Bregman-Wasserstein divergence constraint, and solve for cost-efficient payoffs under benchmark constraints. ...

Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations ArXiv ID: 2311.12239 “View on arXiv” Authors: Unknown Abstract Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of time-dependent PDEs, the dominant paradigm involves casting the approximate solution in terms of stochastic minimization of an objective function given by the norm of the PDE residual, viewed as a function of the neural network parameters. Recently, advancements have been made in the direction of an alternative approach which shares aspects of nonlinearly parametrized Galerkin methods and variational quantum Monte Carlo, especially for high-dimensional, time-dependent PDEs that extend beyond the usual scope of quantum physics. This paper is inspired by the potential of solving Hamilton-Jacobi-Bellman (HJB) PDEs using Neural Galerkin methods and commences the exploration of nonlinearly parametrized trial functions for which the evolution equations are analytically tractable. As a precursor to the Neural Galerkin scheme, we present trial functions with evolution equations that admit closed-form solutions, focusing on time-dependent HJB equations relevant to finance. ...

Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging ArXiv ID: 2401.08600 “View on arXiv” Authors: Unknown Abstract We consider two data driven approaches, Reinforcement Learning (RL) and Deep Trajectory-based Stochastic Optimal Control (DTSOC) for hedging a European call option without and with transaction cost according to a quadratic hedging P&L objective at maturity (“variance-optimal hedging” or “final quadratic hedging”). We study the performance of the two approaches under various market environments (modeled via the Black-Scholes and/or the log-normal SABR model) to understand their advantages and limitations. Without transaction costs and in the Black-Scholes model, both approaches match the performance of the variance-optimal Delta hedge. In the log-normal SABR model without transaction costs, they match the performance of the variance-optimal Barlett’s Delta hedge. Agents trained on Black-Scholes trajectories with matching initial volatility but used on SABR trajectories match the performance of Bartlett’s Delta hedge in average cost, but show substantially wider variance. To apply RL approaches to these problems, P&L at maturity is written as sum of step-wise contributions and variants of RL algorithms are implemented and used that minimize expectation of second moments of such sums. ...

“Centralized or Decentralized?”: Concerns and Value Judgments of Stakeholders in the Non-Fungible Tokens (NFTs) Market ArXiv ID: 2311.10990 “View on arXiv” Authors: Unknown Abstract Non-fungible tokens (NFTs) are decentralized digital tokens to represent the unique ownership of items. Recently, NFTs have been gaining popularity and at the same time bringing up issues, such as scams, racism, and sexism. Decentralization, a key attribute of NFT, contributes to some of the issues that are easier to regulate under centralized schemes, which are intentionally left out of the NFT marketplace. In this work, we delved into this centralization-decentralization dilemma in the NFT space through mixed quantitative and qualitative methods. Centralization-decentralization dilemma is the dilemma caused by the conflict between the slogan of decentralization and the interests of stakeholders. We first analyzed over 30,000 NFT-related tweets to obtain a high-level understanding of stakeholders’ concerns in the NFT space. We then interviewed 15 NFT stakeholders (both creators and collectors) to obtain their in-depth insights into these concerns and potential solutions. Our findings identify concerning issues among users: financial scams, counterfeit NFTs, hacking, and unethical NFTs. We further reflected on the centralization-decentralization dilemma drawing upon the perspectives of the stakeholders in the interviews. Finally, we gave some inferences to solve the centralization-decentralization dilemma in the NFT market and thought about the future of NFT and decentralization. ...

Sector Rotation by Factor Model and Fundamental Analysis ArXiv ID: 2401.00001 “View on arXiv” Authors: Unknown Abstract This study presents an analytical approach to sector rotation, leveraging both factor models and fundamental metrics. We initiate with a systematic classification of sectors, followed by an empirical investigation into their returns. Through factor analysis, the paper underscores the significance of momentum and short-term reversion in dictating sectoral shifts. A subsequent in-depth fundamental analysis evaluates metrics such as PE, PB, EV-to-EBITDA, Dividend Yield, among others. Our primary contribution lies in developing a predictive framework based on these fundamental indicators. The constructed models, post rigorous training, exhibit noteworthy predictive capabilities. The findings furnish a nuanced understanding of sector rotation strategies, with implications for asset management and portfolio construction in the financial domain. ...

Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs) ArXiv ID: 2311.10935 “View on arXiv” Authors: Unknown Abstract The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [“1”]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data. ...

High-Throughput Asset Pricing ArXiv ID: 2311.10685 “View on arXiv” Authors: Unknown Abstract We apply empirical Bayes (EB) to mine data on 136,000 long-short strategies constructed from accounting ratios, past returns, and ticker symbols. This ``high-throughput asset pricing’’ matches the out-of-sample performance of top journals while eliminating look-ahead bias. Naively mining for the largest Sharpe ratios leads to similar performance, consistent with our theoretical results, though EB uniquely provides unbiased predictions with transparent intuition. Predictability is concentrated in accounting strategies, small stocks, and pre-2004 periods, consistent with limited attention theories. Multiple testing methods popular in finance fail to identify most out-of-sample performers. High-throughput methods provide a rigorous, unbiased framework for understanding asset prices. ...

Reinforcement Learning with Maskable Stock Representation for Portfolio Management in Customizable Stock Pools ArXiv ID: 2311.10801 “View on arXiv” Authors: Unknown Abstract Portfolio management (PM) is a fundamental financial trading task, which explores the optimal periodical reallocation of capitals into different stocks to pursue long-term profits. Reinforcement learning (RL) has recently shown its potential to train profitable agents for PM through interacting with financial markets. However, existing work mostly focuses on fixed stock pools, which is inconsistent with investors’ practical demand. Specifically, the target stock pool of different investors varies dramatically due to their discrepancy on market states and individual investors may temporally adjust stocks they desire to trade (e.g., adding one popular stocks), which lead to customizable stock pools (CSPs). Existing RL methods require to retrain RL agents even with a tiny change of the stock pool, which leads to high computational cost and unstable performance. To tackle this challenge, we propose EarnMore, a rEinforcement leARNing framework with Maskable stOck REpresentation to handle PM with CSPs through one-shot training in a global stock pool (GSP). Specifically, we first introduce a mechanism to mask out the representation of the stocks outside the target pool. Second, we learn meaningful stock representations through a self-supervised masking and reconstruction process. Third, a re-weighting mechanism is designed to make the portfolio concentrate on favorable stocks and neglect the stocks outside the target pool. Through extensive experiments on 8 subset stock pools of the US stock market, we demonstrate that EarnMore significantly outperforms 14 state-of-the-art baselines in terms of 6 popular financial metrics with over 40% improvement on profit. ...

Measure of Dependence for Financial Time-Series ArXiv ID: 2311.12129 “View on arXiv” Authors: Unknown Abstract Assessing the predictive power of both data and models holds paramount significance in time-series machine learning applications. Yet, preparing time series data accurately and employing an appropriate measure for predictive power seems to be a non-trivial task. This work involves reviewing and establishing the groundwork for a comprehensive analysis of shaping time-series data and evaluating various measures of dependence. Lastly, we present a method, framework, and a concrete example for selecting and evaluating a suitable measure of dependence. ...

Predicting risk/reward ratio in financial markets for asset management using machine learning ArXiv ID: 2311.09148 “View on arXiv” Authors: Unknown Abstract Financial market forecasting remains a formidable challenge despite the surge in computational capabilities and machine learning advancements. While numerous studies have underscored the precision of computer-generated market predictions, many of these forecasts fail to yield profitable trading outcomes. This discrepancy often arises from the unpredictable nature of profit and loss ratios in the event of successful and unsuccessful predictions. In this study, we introduce a novel algorithm specifically designed for forecasting the profit and loss outcomes of trading activities. This is further augmented by an innovative approach for integrating these forecasts with previous predictions of market trends. This approach is designed for algorithmic trading, enabling traders to assess the profitability of each trade and calibrate the optimal trade size. Our findings indicate that this method significantly improves the performance of traditional trading strategies as well as algorithmic trading systems, offering a promising avenue for enhancing trading decisions. ...