Decoding Market Signals with AI and Economic Logic

by

Author: Denis Avetisyan

A new framework blends deep learning with established economic principles to improve financial forecasting and offer greater transparency into market behavior.

ARTEMIS dissects irregularly sampled market data through a tightly integrated framework-encoding temporal dynamics with a Laplace neural operator, evolving states via a physics-informed stochastic differential equation constrained by no-arbitrage conditions and a bounded Sharpe ratio, distilling these dynamics into interpretable symbolic representations, and ultimately providing distribution-free predictions calibrated via conformal allocation-all optimized through joint training with a consistency loss anchoring the latent trajectory to encoder outputs.
ARTEMIS dissects irregularly sampled market data through a tightly integrated framework-encoding temporal dynamics with a Laplace neural operator, evolving states via a physics-informed stochastic differential equation constrained by no-arbitrage conditions and a bounded Sharpe ratio, distilling these dynamics into interpretable symbolic representations, and ultimately providing distribution-free predictions calibrated via conformal allocation-all optimized through joint training with a consistency loss anchoring the latent trajectory to encoder outputs.

ARTEMIS combines neuro-symbolic AI, physics-informed neural networks, and conformal prediction for robust and interpretable financial time series analysis.

Despite the increasing power of deep learning in quantitative finance, a critical gap remains between predictive accuracy and economically plausible, interpretable strategies. This paper introduces ARTEMIS (Arbitrage-free Representation Through Economic Models and Interpretable Symbolics), a novel neuro-symbolic framework designed to bridge this divide by integrating continuous-time operators, physics-informed regularization, and differentiable symbolic regression. Our results demonstrate that ARTEMIS achieves state-of-the-art directional accuracy across multiple financial datasets, notably outperforming existing methods in challenging regimes like synthetic market crashes. Can this approach unlock a new generation of transparent and robust AI-driven trading systems grounded in fundamental economic principles?

Decoding Market Whispers: The Limits of Conventional Models

Conventional financial time series models frequently fall short when attempting to mirror the true behavior of markets due to an inherent simplification of reality. These models typically treat time as a series of discrete points, overlooking the continuous flow that characterizes trading activity and price formation. This discretization introduces approximation errors, particularly when dealing with high-frequency data or attempting to predict short-term movements. Consequently, predictions based on these models often diverge from actual market outcomes, impacting the reliability of risk assessments and investment strategies. The limitations stem from an inability to fully capture the complex interplay of factors influencing price changes, including order flow, information diffusion, and investor sentiment, all of which evolve continuously rather than in distinct steps. A more nuanced approach, acknowledging the continuous-time nature of financial processes, is therefore essential for improved predictive accuracy and robust financial decision-making.

Many conventional financial models, while computationally efficient, introduce distortions by treating market processes as occurring at discrete points in time – a simplification that overlooks the continuous flow of information and trading. This discretization can lead to inaccuracies, particularly when valuing complex derivatives or assessing risk over extended periods. Furthermore, a significant limitation of some established techniques is the failure to fully integrate the principle of no-arbitrage – the economic concept that riskless profit opportunities should not exist. When these models deviate from no-arbitrage conditions, they can produce unrealistic price predictions and underestimate potential vulnerabilities in financial systems. Consequently, the resulting valuations may be unreliable for crucial decisions regarding asset allocation and risk mitigation, highlighting the need for more sophisticated approaches that accurately reflect the continuous, arbitrage-free nature of financial markets.

The capacity to accurately represent the underlying, often hidden, forces driving financial markets is paramount to effective financial decision-making. Sophisticated risk management strategies depend on a clear understanding of how assets truly behave, going beyond superficial observations; a precise model of latent dynamics allows for more reliable quantification of potential losses. Similarly, the fair valuation of derivative instruments – contracts whose value is derived from an underlying asset – hinges on an accurate projection of future price movements, a task significantly improved by incorporating these hidden market drivers. Finally, portfolio optimization, the process of constructing an investment portfolio to maximize returns for a given level of risk, benefits immensely from models that can anticipate how different assets will interact and respond to changing market conditions, ultimately leading to more robust and profitable investment strategies.

Analysis of the model's latent space on the DSLOB crash-regime test set reveals economically interpretable stochastic dynamics, with increasing diffusion magnitude <span class="katex-eq" data-katex-display="false">||\boldsymbol{\sigma}(\mathbf{Z},t)||</span> indicating growing uncertainty towards the end of the prediction window and a peaked drift magnitude <span class="katex-eq" data-katex-display="false">||\boldsymbol{\mu}(\mathbf{Z},t)||</span> reflecting learned momentum and mean-reversion, both emerging from physics-based regularisation without explicit supervision.
Analysis of the model’s latent space on the DSLOB crash-regime test set reveals economically interpretable stochastic dynamics, with increasing diffusion magnitude ||\boldsymbol{\sigma}(\mathbf{Z},t)|| indicating growing uncertainty towards the end of the prediction window and a peaked drift magnitude ||\boldsymbol{\mu}(\mathbf{Z},t)|| reflecting learned momentum and mean-reversion, both emerging from physics-based regularisation without explicit supervision.

ARTEMIS: Reconstructing Time’s Flow

ARTEMIS utilizes Laplace Neural Operators (LNOs) to address the challenges of irregularly sampled financial time series data. Traditional time series analysis often requires uniformly spaced data, which is uncommon in financial markets due to trading halts, overnight closures, and varying reporting frequencies. LNOs provide a method to directly learn operators that map functions from time to time, effectively creating a continuous representation from discrete and irregularly spaced observations. This is achieved by representing the time series as a function and learning the \$\in t_{0}^{t} K(t,s)f(s)ds\$ integral operator with a neural network, where K(t,s) is the kernel and f(s) represents the time series. The resulting continuous representation allows for accurate modeling and prediction even with incomplete or unevenly spaced data, bypassing the need for imputation or resampling techniques.

ARTEMIS utilizes Neural Stochastic Differential Equations (SDEs) to model the underlying, often unobserved, dynamics of financial markets. Traditional financial models frequently rely on discrete-time representations, which can introduce inaccuracies when dealing with the continuous flow of market data. Neural SDEs, however, offer a continuous-time approach, enabling the framework to capture the inherent randomness and volatility characteristic of financial systems. Specifically, these equations define the probabilistic evolution of latent state variables, described by a drift coefficient and a diffusion coefficient, both parameterized by neural networks. This allows ARTEMIS to learn complex, non-linear relationships within the data and generate more realistic simulations of market behavior, accounting for phenomena like price diffusion and unpredictable shocks, represented mathematically as dX_t = \mu(\theta, X_t) dt + \sigma(\theta, X_t) dW_t , where θ represents the neural network parameters, and dW_t is a Wiener process.

ARTEMIS integrates the capabilities of neural networks – specifically their proficiency in pattern recognition and function approximation from large datasets – with the formal rigor of symbolic reasoning derived from economic theory. This integration is achieved through the use of Neural Stochastic Differential Equations (SDEs) and Laplace Neural Operators, which allow the framework to learn from irregularly sampled financial data while maintaining adherence to established economic principles. Consequently, ARTEMIS moves beyond purely data-driven models by incorporating prior knowledge and constraints, and conversely, offers a data-driven approach to validating and refining theoretical economic models, facilitating a synergistic relationship between empirical observation and theoretical understanding.

The learned stochastic dynamics exhibit a temporally evolving vector field-shifting from inward-pointing, low-volatility behavior at early times <span class="katex-eq" data-katex-display="false">t=0.1</span> to a rotating, high-volatility structure at later times <span class="katex-eq" data-katex-display="false">t=0.9</span>, particularly in regions representing volatile market conditions-reflecting the influence of HJB-PDE regularization on the learned drift and diffusion processes.
The learned stochastic dynamics exhibit a temporally evolving vector field-shifting from inward-pointing, low-volatility behavior at early times t=0.1 to a rotating, high-volatility structure at later times t=0.9, particularly in regions representing volatile market conditions-reflecting the influence of HJB-PDE regularization on the learned drift and diffusion processes.

Enforcing Order: Economic Consistency and Interpretability

The ARTEMIS model utilizes a Feynman-Kac partial differential equation (PDE) residual loss, termed PDE_Loss, to maintain economic consistency within its predictions. This loss function directly enforces no-arbitrage conditions by penalizing deviations from the theoretical pricing implied by the Black-Scholes equation and related models. Specifically, the PDE_Loss calculates the residual error resulting from solving the underlying PDE and minimizing this error during training ensures that predicted asset prices and hedging strategies adhere to fundamental economic principles, thereby preventing the generation of unrealistic or exploitable predictions. This approach differs from traditional regression-based methods which do not inherently account for these economic constraints.

The ARTEMIS model incorporates a Market Price of Risk (MPR) penalty, denoted as MPR_{Penalty}, to directly influence the instantaneous Sharpe ratio of generated portfolios. This penalty functions by discouraging predictions that result in unrealistically high Sharpe ratios, thereby promoting portfolios with more reasonable risk-adjusted returns. Specifically, the MPR_{Penalty} term is applied during training to constrain the model’s output, ensuring that predicted portfolio returns are appropriately compensated for the level of risk taken; a higher risk portfolio must exhibit commensurately higher expected returns to avoid penalty. This mechanism prevents the model from exploiting statistical noise to generate artificially inflated performance metrics, leading to more stable and economically plausible predictions.

Differentiable symbolic regression within ARTEMIS extracts interpretable mathematical expressions from the learned latent dynamics of the financial model. This process utilizes automatic differentiation to optimize the symbolic regression, identifying key variables and their relationships that govern price formation. The resulting expressions, typically in the form of f(x) = a_0 + a_1x_1 + a_2x_2 + ... , provide a transparent representation of the model’s internal logic, allowing analysts to directly observe how specific market factors influence predicted outcomes and offering insights into the underlying drivers of market behavior beyond a black-box prediction.

ARTEMIS demonstrates leading performance in predicting asset price direction, achieving 64.96% directional accuracy on the highly granular Direct Simulation of Limit Order Book (DSLob) dataset and 96.0% accuracy on the Time-Integrated Market Microstructure (Time-IMM) dataset. These results, obtained across distinct market data sources – DSLOB representing order book dynamics and Time-IMM focusing on trade-based features – indicate the model’s adaptability and robustness to variations in market microstructure and data representation. The performance benchmarks establish ARTEMIS as a state-of-the-art solution for short-term price movement prediction, exceeding the accuracy of existing models on these standard datasets.

Across increasingly volatile market regimes-from normal conditions through stress testing to a crash scenario-ARTEMIS (bold indigo) demonstrates superior robustness, exhibiting minimal performance degradation in Rank IC and Directional Accuracy compared to models lacking temporal depth (Chronos-2) or relying solely on attention (Transformer).
Across increasingly volatile market regimes-from normal conditions through stress testing to a crash scenario-ARTEMIS (bold indigo) demonstrates superior robustness, exhibiting minimal performance degradation in Rank IC and Directional Accuracy compared to models lacking temporal depth (Chronos-2) or relying solely on attention (Transformer).

Beyond Prediction: Navigating Uncertainty with Confidence

ARTEMIS incorporates ConformalPrediction, a powerful technique that moves beyond point forecasts to deliver prediction intervals accompanied by rigorously quantified uncertainty. This statistical approach doesn’t rely on assumptions about the underlying data distribution; instead, it assesses forecast reliability based on the observed calibration error of past predictions. The result is a measure of confidence – a guaranteed coverage level – indicating the probability that the true future value will fall within the generated interval. Consequently, users receive not just a prediction, but also an assessment of its trustworthiness, which is crucial for risk-aware applications where understanding the limits of forecast accuracy is paramount. This framework enables more informed decision-making by explicitly acknowledging and quantifying the inherent uncertainty in financial forecasting.

ARTEMIS distinguishes itself by moving beyond point forecasts to deliver probabilistic predictions, a crucial advancement for navigating financial uncertainty. Rather than simply predicting a single future value, the model generates a range of possible outcomes, each associated with a specific probability. This allows risk managers and investors to assess not just what might happen, but also the likelihood of various scenarios, enabling more nuanced and data-driven decision-making. By quantifying the potential for both gains and losses, ARTEMIS facilitates the construction of robust portfolios and hedging strategies tailored to specific risk tolerances, ultimately fostering more informed capital allocation and improved financial outcomes in inherently unpredictable markets.

ARTEMIS leverages the EulerMaruyama scheme to efficiently simulate the stochastic differential equations (SDEs) that underpin financial modeling. This numerical method approximates the continuous-time SDE by discretizing it into a series of time steps, allowing for computation on standard digital hardware. Unlike more complex methods, EulerMaruyama offers a favorable balance between accuracy and computational cost, making it particularly suitable for real-time forecasting and risk assessment. The scheme’s simplicity enables rapid simulations, crucial when dealing with the high dimensionality and frequent updates characteristic of financial time series, while maintaining a reasonable level of precision in representing the inherent randomness of market behavior. This efficient simulation capability is central to ARTEMIS’s ability to generate probabilistic forecasts and quantify uncertainty in a timely manner.

The model’s reliance on economically plausible predictions is demonstrably strong; research indicates that removing the partial differential equation (PDE) loss function – a component enforcing these economic constraints – leads to a substantial decline in directional accuracy. Specifically, the model’s ability to correctly predict market direction fell from 64.89% to 50.32% when this constraint was lifted. This significant reduction underscores the critical role of incorporating established economic principles into the forecasting framework, suggesting that purely data-driven approaches, while potentially capturing short-term patterns, require these foundational constraints to generate consistently reliable and economically sound predictions.

ARTEMIS demonstrates superior predictive performance on the DSLOB crash-regime test set, exhibiting the tightest concentration of predicted versus actual mid-price returns along the identity line and achieving the highest Rank IC, while Chronos-2, as a zero-shot baseline, displays the poorest performance with highly dispersed predictions.
ARTEMIS demonstrates superior predictive performance on the DSLOB crash-regime test set, exhibiting the tightest concentration of predicted versus actual mid-price returns along the identity line and achieving the highest Rank IC, while Chronos-2, as a zero-shot baseline, displays the poorest performance with highly dispersed predictions.

ARTEMIS, as detailed in the research, actively challenges the conventional boundaries of financial forecasting. It isn’t simply about achieving incremental improvements in accuracy; it’s about fundamentally re-examining how predictions are made, integrating established economic principles with the flexibility of deep learning. This spirit aligns perfectly with the ethos of Ken Thompson, who once stated, “Software is a craft, and like any craft, there is an inherent beauty in doing things well.” ARTEMIS embodies this sentiment, crafting a system where transparency and robustness aren’t afterthoughts, but integral components-a testament to the power of thoughtfully designed systems that seek to understand, and even reconstruct, the underlying realities they model. The framework’s use of symbolic regression, in particular, speaks to a desire to distill complex dynamics into interpretable rules, mirroring a dedication to clarity and elegant solutions.

What Lies Ahead?

ARTEMIS, in its attempt to yoke the predictive power of deep learning to the rigor of economic modeling, predictably reveals more questions than answers. The framework’s success hinges on a transparent coupling of data-driven discovery with established theory, yet the very act of distillation – forcing complex dynamics into symbolic form – introduces a vulnerability. The resulting equations, while interpretable, represent approximations, and the error introduced by this simplification remains a critical point for further investigation. True security lies not in believing the model is the market, but in understanding how it diverges.

The current implementation, focused on financial time series, serves as a useful proving ground. However, the underlying principles-integrating physics-informed neural networks with symbolic regression for constrained optimization-are not domain-specific. The next logical step involves applying this neuro-symbolic approach to systems where the governing equations are less known, or actively concealed. Consider, for instance, reverse-engineering the dynamics of complex networks – social, biological, or even adversarial – where the ‘rules’ are emergent, not explicitly defined.

Ultimately, the value of ARTEMIS, and frameworks like it, isn’t solely in improved forecasting. It’s in the systematic dismantling of the black box. Conformal prediction offers a statistically rigorous means of quantifying uncertainty, but the real challenge remains: to build models that fail gracefully, revealing their limitations rather than masking them with spurious precision. The pursuit of knowledge, after all, isn’t about finding the right answer; it’s about rigorously exploring the boundaries of what cannot be known.

Original article: https://arxiv.org/pdf/2603.18107.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-03-20 09:51