On Accelerating Large-Scale Robust Portfolio Optimization ArXiv ID: 2408.07879 “View on arXiv” Authors: Unknown Abstract Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we propose an extended supporting hyperplane approximation approach for efficiently solving a class of distributionally robust portfolio problems for a general class of additively separable utility functions and polyhedral ambiguity distribution set, applied to a large-scale set of assets. Our technique is validated using a large-scale portfolio of the S&P 500 index constituents, demonstrating robust out-of-sample trading performance. More importantly, our empirical studies show that this approach significantly reduces computational time compared to traditional concave Expected Log-Growth (ELG) optimization, with running times decreasing from several thousand seconds to just a few. This method provides a scalable and practical solution to large-scale robust portfolio optimization, addressing both theoretical and practical challenges. ...

Forecasting stock return distributions around the globe with quantile neural networks ArXiv ID: 2408.07497 “View on arXiv” Authors: Unknown Abstract We propose a novel machine learning approach for forecasting the distribution of stock returns using a rich set of firm-level and market predictors. Our method combines a two-stage quantile neural network with spline interpolation to construct smooth, flexible cumulative distribution functions without relying on restrictive parametric assumptions. This allows accurate modelling of non-Gaussian features such as fat tails and asymmetries. Furthermore, we show how to derive other statistics from the forecasted return distribution such as mean, variance, skewness, and kurtosis. The derived mean and variance forecasts offer significantly improved out-of-sample performance compared to standard models. We demonstrate the robustness of the method in US and international markets. ...

Model-based and empirical analyses of stochastic fluctuations in economy and finance ArXiv ID: 2408.16010 “View on arXiv” Authors: Unknown Abstract The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis concerns statistical-based modeling and empirical analyses with applications in finance, forecasting, production processes and game theory. In these areas the time dependence of probability distributions is of prime interest and can be measured or exactly calculated for model systems. The correlation coefficients and moments are among the useful quantities to describe the dynamics and the correlations between random variables. However, the full investigation can only be achieved if the probability distribution function of the variable is known; its derivation is one of the main focuses of the present work. ...

Modeling of Measurement Error in Financial Returns Data ArXiv ID: 2408.07405 “View on arXiv” Authors: Unknown Abstract In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [“12”] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. ...

Portfolio and reinsurance optimization under unknown market price of risk ArXiv ID: 2408.07432 “View on arXiv” Authors: Unknown Abstract We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control problem under the observation filtration only, the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton-Jacobi-Bellman equation, and to provide explicit formulas for the value function and the optimal investment-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments. ...

Stylized facts in Web3 ArXiv ID: 2408.07653 “View on arXiv” Authors: Unknown Abstract This paper presents a comprehensive statistical analysis of the Web3 ecosystem, comparing various Web3 tokens with traditional financial assets across multiple time scales. We examine probability distributions, tail behaviors, and other key stylized facts of the returns for a diverse range of tokens, including decentralized exchanges, liquidity pools, and centralized exchanges. Despite functional differences, most tokens exhibit well-established empirical facts, including unconditional probability density of returns with heavy tails gradually becoming Gaussian and volatility clustering. Furthermore, we compare assets traded on centralized (CEX) and decentralized (DEX) exchanges, finding that DEXs exhibit similar stylized facts despite different trading mechanisms and often divergent long-term performance. We propose that this similarity is attributable to arbitrageurs striving to maintain similar centralized and decentralized prices. Our study contributes to a better understanding of the dynamics of Web3 tokens and the relationship between CEX and DEX markets, with important implications for risk management, pricing models, and portfolio construction in the rapidly evolving DeFi landscape. These results add to the growing body of literature on cryptocurrency markets and provide insights that can guide the development of more accurate models for DeFi markets. ...

Case-based Explainability for Random Forest: Prototypes, Critics, Counter-factuals and Semi-factuals ArXiv ID: 2408.06679 “View on arXiv” Authors: Unknown Abstract The explainability of black-box machine learning algorithms, commonly known as Explainable Artificial Intelligence (XAI), has become crucial for financial and other regulated industrial applications due to regulatory requirements and the need for transparency in business practices. Among the various paradigms of XAI, Explainable Case-Based Reasoning (XCBR) stands out as a pragmatic approach that elucidates the output of a model by referencing actual examples from the data used to train or test the model. Despite its potential, XCBR has been relatively underexplored for many algorithms such as tree-based models until recently. We start by observing that most XCBR methods are defined based on the distance metric learned by the algorithm. By utilizing a recently proposed technique to extract the distance metric learned by Random Forests (RFs), which is both geometry- and accuracy-preserving, we investigate various XCBR methods. These methods amount to identify special points from the training datasets, such as prototypes, critics, counter-factuals, and semi-factuals, to explain the predictions for a given query of the RF. We evaluate these special points using various evaluation metrics to assess their explanatory power and effectiveness. ...

Harnessing Earnings Reports for Stock Predictions: A QLoRA-Enhanced LLM Approach ArXiv ID: 2408.06634 “View on arXiv” Authors: Unknown Abstract Accurate stock market predictions following earnings reports are crucial for investors. Traditional methods, particularly classical machine learning models, struggle with these predictions because they cannot effectively process and interpret extensive textual data contained in earnings reports and often overlook nuances that influence market movements. This paper introduces an advanced approach by employing Large Language Models (LLMs) instruction fine-tuned with a novel combination of instruction-based techniques and quantized low-rank adaptation (QLoRA) compression. Our methodology integrates ‘base factors’, such as financial metric growth and earnings transcripts, with ’external factors’, including recent market indices performances and analyst grades, to create a rich, supervised dataset. This comprehensive dataset enables our models to achieve superior predictive performance in terms of accuracy, weighted F1, and Matthews correlation coefficient (MCC), especially evident in the comparison with benchmarks such as GPT-4. We specifically highlight the efficacy of the llama-3-8b-Instruct-4bit model, which showcases significant improvements over baseline models. The paper also discusses the potential of expanding the output capabilities to include a ‘Hold’ option and extending the prediction horizon, aiming to accommodate various investment styles and time frames. This study not only demonstrates the power of integrating cutting-edge AI with fine-tuned financial data but also paves the way for future research in enhancing AI-driven financial analysis tools. ...

The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency ArXiv ID: 2408.06661 “View on arXiv” Authors: Unknown Abstract In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular variation models on the entirety of $\mathbb{“R”}^d$ and develop a bivariate measure for asymmetry in the strength of extremal dependence between adjacent orthants. Our directional tail dependence (DTD) measure allows us to define the Efficient Tail Hypothesis (ETH) – an analogue of the Efficient Market Hypothesis – for the extremal behaviour of the market. Asymptotic results for estimators of DTD are described, and we discuss testing of the ETH via permutation-based methods and present novel tools for visualization. Empirical study of China’s futures market leads to a rejection of the ETH and we identify potential profitable investment opportunities. To promote the research of microstructure in China’s derivatives market, we open-source our high-frequency data, which are being collected continuously from multiple derivative exchanges. ...

Adaptive Multilevel Stochastic Approximation of the Value-at-Risk ArXiv ID: 2408.06531 “View on arXiv” Authors: Unknown Abstract Crépey, Frikha, and Louzi (2023) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. The optimal complexity of the scheme is in $O({"\varepsilon"}^{"-5/2"})$, ${"\varepsilon"} > 0$ being a prescribed accuracy, which is suboptimal when compared to the canonical multilevel Monte Carlo performance. This suboptimality stems from the discontinuity of the Heaviside function involved in the biased stochastic gradient that is recursively evaluated to derive the value-at-risk. To mitigate this issue, this paper proposes and analyzes a multilevel stochastic approximation algorithm that adaptively selects the number of inner samples at each level, and proves that its optimal complexity is in $O({"\varepsilon"}^{"-2"}|\ln {"\varepsilon"}|^{“5/2”})$. Our theoretical analysis is exemplified through numerical experiments. ...