Risk Aggregation and Allocation in the Presence of Systematic Risk via Stable Laws ArXiv ID: 2410.14984 “View on arXiv” Authors: Unknown Abstract In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well understood. Certainly, Insurers and Financiers are interested in the properties of the sums of the risks they are exposed to and the dependence of risks therein. Realistic risk models however must account for a variety of phenomena: ill-defined moments, lack of elliptical dependence structures, excess kurtosis and highly heterogeneous marginals. Equally important is the concern over industry-wide systematic risks that can affect multiple business lines at once. Many techniques of varying sophistication have been developed with all or some of these problems in mind. We propose a modification to the classical individual risk model that allows us to model company-wide losses via the class of Multivariate Stable Distributions. Stable Distributions incorporate many of the unpleasant features required for a realistic risk model while maintaining tractable aggregation and dependence results. We additionally compute the Tail Conditional Expectation of aggregate risks within the model and the corresponding allocations. ...

Dynamic Factor Allocation Leveraging Regime-Switching Signals ArXiv ID: 2410.14841 “View on arXiv” Authors: Unknown Abstract This article explores dynamic factor allocation by analyzing the cyclical performance of factors through regime analysis. The authors focus on a U.S. equity investment universe comprising seven long-only indices representing the market and six style factors: value, size, momentum, quality, low volatility, and growth. Their approach integrates factor-specific regime inferences of each factor index’s active performance relative to the market into the Black-Litterman model to construct a fully-invested, long-only multi-factor portfolio. First, the authors apply the sparse jump model (SJM) to identify bull and bear market regimes for individual factors, using a feature set based on risk and return measures from historical factor active returns, as well as variables reflecting the broader market environment. The regimes identified by the SJM exhibit enhanced stability and interpretability compared to traditional methods. A hypothetical single-factor long-short strategy is then used to assess these regime inferences and fine-tune hyperparameters, resulting in a positive Sharpe ratio of this strategy across all factors with low correlation among them. These regime inferences are then incorporated into the Black-Litterman framework to dynamically adjust allocations among the seven indices, with an equally weighted (EW) portfolio serving as the benchmark. Empirical results show that the constructed multi-factor portfolio significantly improves the information ratio (IR) relative to the market, raising it from just 0.05 for the EW benchmark to approximately 0.4. When measured relative to the EW benchmark itself, the dynamic allocation achieves an IR of around 0.4 to 0.5. The strategy also enhances absolute portfolio performance across key metrics such as the Sharpe ratio and maximum drawdown. ...

Neuro-Symbolic Traders: Assessing the Wisdom of AI Crowds in Markets ArXiv ID: 2410.14587 “View on arXiv” Authors: Unknown Abstract Deep generative models are becoming increasingly used as tools for financial analysis. However, it is unclear how these models will influence financial markets, especially when they infer financial value in a semi-autonomous way. In this work, we explore the interplay between deep generative models and market dynamics. We develop a form of virtual traders that use deep generative models to make buy/sell decisions, which we term neuro-symbolic traders, and expose them to a virtual market. Under our framework, neuro-symbolic traders are agents that use vision-language models to discover a model of the fundamental value of an asset. Agents develop this model as a stochastic differential equation, calibrated to market data using gradient descent. We test our neuro-symbolic traders on both synthetic data and real financial time series, including an equity stock, commodity, and a foreign exchange pair. We then expose several groups of neuro-symbolic traders to a virtual market environment. This market environment allows for feedback between the traders belief of the underlying value to the observed price dynamics. We find that this leads to price suppression compared to the historical data, highlighting a future risk to market stability. Our work is a first step towards quantifying the effect of deep generative agents on markets dynamics and sets out some of the potential risks and benefits of this approach in the future. ...

Reinforcement Learning in Non-Markov Market-Making ArXiv ID: 2410.14504 “View on arXiv” Authors: Unknown Abstract We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used, where we deployed the state-of-the-art Soft Actor-Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces like in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment for simulating this strategy. Here we also give an in-depth overview of the jump-diffusion pricing dynamics used, our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss training and testing results, where we give visuals of how important deterministic and stochastic processes such as the bid/ask, trade executions, inventory, and the reward function evolved. We include a discussion on the limitations of these results, which are important points to note for most diffusion models in this setting. ...

Simultaneously Solving FBSDEs and their Associated Semilinear Elliptic PDEs with Small Neural Operators ArXiv ID: 2410.14788 “View on arXiv” Authors: Unknown Abstract Forward-backwards stochastic differential equations (FBSDEs) play an important role in optimal control, game theory, economics, mathematical finance, and in reinforcement learning. Unfortunately, the available FBSDE solvers operate on \textit{“individual”} FBSDEs, meaning that they cannot provide a computationally feasible strategy for solving large families of FBSDEs, as these solvers must be re-run several times. \textit{“Neural operators”} (NOs) offer an alternative approach for \textit{“simultaneously solving”} large families of decoupled FBSDEs by directly approximating the solution operator mapping \textit{“inputs:”} terminal conditions and dynamics of the backwards process to \textit{“outputs:”} solutions to the associated FBSDE. Though universal approximation theorems (UATs) guarantee the existence of such NOs, these NOs are unrealistically large. Upon making only a few simple theoretically-guided tweaks to the standard convolutional NO build, we confirm that ``small’’ NOs can uniformly approximate the solution operator to structured families of FBSDEs with random terminal time, uniformly on suitable compact sets determined by Sobolev norms using a logarithmic depth, a constant width, and a polynomial rank in the reciprocal approximation error. This result is rooted in our second result, and main contribution to the NOs for PDE literature, showing that our convolutional NOs of similar depth and width but grow only \textit{“quadratically”} (at a dimension-free rate) when uniformly approximating the solution operator of the associated class of semilinear Elliptic PDEs to these families of FBSDEs. A key insight into how NOs work we uncover is that the convolutional layers of our NO can approximately implement the fixed point iteration used to prove the existence of a unique solution to these semilinear Elliptic PDEs. ...

Competitive equilibria in trading ArXiv ID: 2410.13583 “View on arXiv” Authors: Unknown Abstract This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of results in that paper center on the two traders in competition and equilibrium results are presented. The second paper, introduces computational methods based on Fourier Series which allows the introduction of a broad range of constraints into the optimal strategies derived. The current paper returns to the unconstrained case and provides a complete solution to finding equilibrium strategies in competition and handles completely arbitrary situations. As a result we present a detailed analysis of the value (or not) of trade centralization and we show that firms who naively centralize trades do not generally benefit and sometimes, in fact, lose. On the other hand, firms that strategically centralize their trades generally will be able to benefit. ...

Concentrated Superelliptical Market Maker ArXiv ID: 2410.13265 “View on arXiv” Authors: Unknown Abstract An automated market maker where the price can cross the zero bound into the negative price domain with applications in electricity, energy, and derivatives markets is presented. A unique feature involves the ability to swap both negatively and positively priced assets between one another, which unlike traditional markets requires a numeraire in the form of a currency. Model extensions to skew and concentrate liquidity are shown. The liquidity fingerprint, payoff, and invariant are compared to the Black-Scholes covered call and the Logarithmic Market Scoring Rule invariants. ...

UCFE: A User-Centric Financial Expertise Benchmark for Large Language Models ArXiv ID: 2410.14059 “View on arXiv” Authors: Unknown Abstract This paper introduces the UCFE: User-Centric Financial Expertise benchmark, an innovative framework designed to evaluate the ability of large language models (LLMs) to handle complex real-world financial tasks. UCFE benchmark adopts a hybrid approach that combines human expert evaluations with dynamic, task-specific interactions to simulate the complexities of evolving financial scenarios. Firstly, we conducted a user study involving 804 participants, collecting their feedback on financial tasks. Secondly, based on this feedback, we created our dataset that encompasses a wide range of user intents and interactions. This dataset serves as the foundation for benchmarking 11 LLMs services using the LLM-as-Judge methodology. Our results show a significant alignment between benchmark scores and human preferences, with a Pearson correlation coefficient of 0.78, confirming the effectiveness of the UCFE dataset and our evaluation approach. UCFE benchmark not only reveals the potential of LLMs in the financial domain but also provides a robust framework for assessing their performance and user satisfaction. ...

TradExpert: Revolutionizing Trading with Mixture of Expert LLMs ArXiv ID: 2411.00782 “View on arXiv” Authors: Unknown Abstract The integration of Artificial Intelligence (AI) in the financial domain has opened new avenues for quantitative trading, particularly through the use of Large Language Models (LLMs). However, the challenge of effectively synthesizing insights from diverse data sources and integrating both structured and unstructured data persists. This paper presents TradeExpert, a novel framework that employs a mix of experts (MoE) approach, using four specialized LLMs, each analyzing distinct sources of financial data, including news articles, market data, alpha factors, and fundamental data. The insights of these expert LLMs are further synthesized by a General Expert LLM to make a final prediction or decision. With specific prompts, TradeExpert can be switched between the prediction mode and the ranking mode for stock movement prediction and quantitative stock trading, respectively. In addition to existing benchmarks, we also release a large-scale financial dataset to comprehensively evaluate TradeExpert’s effectiveness. Our experimental results demonstrate TradeExpert’s superior performance across all trading scenarios. ...

Clustering Digital Assets Using Path Signatures: Application to Portfolio Construction ArXiv ID: 2410.23297 “View on arXiv” Authors: Unknown Abstract We propose a new way of building portfolios of cryptocurrencies that provide good diversification properties to investors. First, we seek to filter these digital assets by creating some clusters based on their path signature. The goal is to identify similar patterns in the behavior of these highly volatile assets. Once such clusters have been built, we propose “optimal” portfolios by comparing the performances of such portfolios to a universe of unfiltered digital assets. Our intuition is that clustering based on path signatures will make it easier to capture the main trends and features of a group of cryptocurrencies, and allow parsimonious portfolios that reduce excessive transaction fees. Empirically, our assumptions seem to be satisfied. ...