arXiv subjects

Alejandro Rodriguez Dominguez

Publications and source records attributed to Alejandro Rodriguez Dominguez.

At least 19 recordsLinked to original sources

arXiv2026

Switching Frictions, Heterogeneous Trading Horizons, and Long-Memory Order Flow

This paper develops a mechanism through which costly changes in the representations used for portfolio choice can contribute to persistent signed order flow. Heterogeneous switching thresholds and opportunity volatility generate heterogeneous residence times, and renewal aggregation maps their execution-weighted tail into the decay of aggregate flow covariance. Under common execution weights, the same tail determines the exponent of representation-spell durations, the order-flow memory exponent, and the horizon at which finite-market scaling must end. First-passage renewal analysis establishes these joint restrictions. Structural simulations recover them from realized paths, quantify the distortion created by mismatched weights, and show how finite cross sections shorten the usable inference horizon. The resulting empirical protocol converts an aggregate persistence fit into cross-dataset restrictions that can determine whether a duration-based kernel is suitable for a separate execution-cost model.

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arXiv2026

Uniform Inference and Certified Capacity at a Reflexive Stability Boundary

This paper develops uniform inference and certified capacity decisions for an estimated financial stability boundary. Conditional risk, temporary cross-impact, and effective risk-bearing capacity are jointly estimated from dependent observations. Conventional pointwise inference is reliable at a separated simple spectral root but can fail near semisimple or defective collisions. Projecting a valid joint confidence region for the underlying inputs avoids this local approximation and yields a three-way regime decision with abstention and a one-sided capacity bound. A verified two-dimensional implementation keeps numerical error from creating a resolved sign. Structural simulations recover the predicted tradeoff between coverage and resolution, while observed-risk stresses distinguish statistical abstention from an insufficient computational budget. The financial conclusions remain conditional on the identification of cross-impact, the normalization of capacity, and stability of the inputs over the action horizon.

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arXiv2026

The Market's Conditioning Representation: Equilibrium, Crowding, and Convention Multiplicity

Asset-pricing models typically condition on a fixed information set. This paper endogenises the market's conditioning architecture by allowing portfolios to choose representations whose induced exposures affect prices. Capital allocated across representations determines aggregate positions and the clearing premium, while price feedback changes representation value and, through causal certification, admissible representations. A representation equilibrium is the fixed point of this configuration--price--certification loop. The framework separates position crowding through market impact from representation crowding generated by driver-space overlap and priced through a basis-invariant information-capacity cost. Under compactness, resolvent regularity and continuous certification, equilibrium exists at every switching cost; within a stable certification cell, informational congestion yields a concave population game and local uniqueness under a small-gain condition. At a settled configuration, a spectral statistic combining cross-impact, covariance and deployed capacity determines three position-path regimes: below one half the fundamental solution is unique; at the boundary only innovation-free deviations remain; above it, destabilising directions support a continuum of self-confirming conventions. Monotone impact lies inside the uniqueness region, while indefinite impact alone is not sufficient for multiplicity. Intermediary hedging can generate an indefinite response while round trips remain costly. Endogenous risk capacity bounds convention amplitudes, and least-squares learning makes the dominant convention neutral rather than attracting. The threshold is not estimated in data; instead, the empirical exercise documents an out-of-sample, driver-specific signature consistent with representation crowding and states the conditions required for direct measurement.

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arXiv2026

Robustness or Crowding: Experimental Design for Trading Strategy Capacity

How much capital a trading strategy can absorb before its edge disappears is a causal question about how much is deployed, but it is answered with observational proxies that rest on incompatible assumptions. We ask what experiment would answer it instead, and show that two features of the problem interact to constrain any answer. Deployed capital erodes the edge gradually, so a trial of fixed length measures less than the eventual effect; and parallel implementations of one strategy trade the same securities, so they are not independent units. Comparing implementations on the same date removes market-wide shocks, which is what makes the comparison credible. But the crowding created by the strategy's own accumulated position is common to those implementations too, and an arbitrary date effect absorbs it exactly: the comparison that makes the experiment robust is the one that prevents it from measuring the crowding capacity is about. A same-date design recovers one implementation's private response at the prevailing level of aggregate positioning, and reaching the aggregate effect requires either implementations with deliberately different exposure to that position or variation in it over time. We characterise what each route identifies and what it costs, establish how far a fixed holding period understates the eventual effect and how to correct for it, and show what a finite set of deployment levels can and cannot reveal. A calibration on a purpose-built panel illustrates the resulting design rules and prices a study that would follow them.

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arXiv2026

Dynamic Causal Portfolio Choice: Hedging the Rotation of the Common-Driver Manifold

When a portfolio is conditioned on a minimal set of observable drivers under which its assets become mutually independent over the investment horizon, the dynamic investment problem acquires a distinctive geometric structure. We study continuous-time portfolio choice in this setting. The conditioning representation, rather than the asset vector, becomes the natural state of the problem, and it moves: the sensitivity of returns to the drivers depends on the state, the conditioning set may itself change over time, and the induced information geometry both rotates and, at discrete instants, jumps. The optimal policy separates into a static component that allocates along the conditioning geometry at each instant and an intertemporal component that hedges the predictable motion of that geometry, a first-order effect in the model rather than a refinement, placing the coordinates of the information geometry in the role played by exogenous state variables in classical intertemporal asset pricing. Because the problem is organized by the drivers, its computational cost is governed by their number rather than by the number of assets. Changes in the conditioning set generate a risk that continuous trading cannot span, so the market is incomplete in the direction of its own geometry. The analysis is carried out in a controlled diffusion model, and the resulting structure is illustrated on synthetic economies designed to isolate each mechanism.

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arXiv2026

Screening-Off Information and Conditional Risk in Portfolio Choice

Conditional portfolio models estimate risk relative to a chosen information set, yet rarely test whether that information removes common cross-asset dependence. When it does not, systematic risk may be treated as idiosyncratic, distorting portfolios and attainable efficient frontiers. We formulate this prior problem as screening-off for portfolio choice. A hierarchy separates causal, distributional and second-moment requirements, while an exact covariance decomposition distinguishes represented systematic response, omitted response risk and residual cross-asset dependence. The two representation errors have different financial implications: omitted response necessarily overstates attainable mean--variance opportunities, whereas incomplete screening can distort them in either direction. Exact finite perturbation identities and non-asymptotic bounds map both errors into changes in constrained portfolio weights and frontier potential. Controlled experiments verify the mechanisms under static, heavy-tailed, dynamic and nonlinear designs. Frozen out-of-sample market tests combine a broad universe of observable economic and financial drivers with 150 U.S. equities and 17 hedge-fund strategy indices. Compact selected representations materially reduce residual dependence in both panels; in equities, residual-aware covariance estimation improves materially on the uncorrected diagonal-residual restriction while remaining competitive with established covariance regularizers. The framework provides a falsifiable information criterion for conditional risk and a direct map from representation failure to portfolio instability.

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arXiv2026

A sharp order-three obstruction to the aggregation of conditional price-of-risk attribution

We study the squared price-of-risk premium of a portfolio -- an integrated conditional squared Sharpe-ratio functional, not an expected excess return -- and its attribution to causal drivers. Relative to a declared admissible benchmark it decomposes into intervention-stable premium, a signed causal distortion (the confounding wedge), and a nonnegative information loss; the loss is an $L^2$ projection residual, the wedge is not. The decomposition is well posed exactly when the driver filtration is immersed in the price filtration. It need not aggregate across portfolios pooling drivers: we identify an order-three obstruction that is invisible to every singleton and pairwise admissibility screen -- each one- and two-driver sub-book is immersed while the pooled triple reveals a future innovation -- the analogue of Bernstein's pairwise-but-not-mutually-independent triple, and minimal relative to such pairwise diagnostics. We separate its two ingredients, combinatorial masking and anticipative coupling. The failure is one of immersion, not of no-arbitrage. Experiments on synthetic single- and multi-driver panels show the decomposition and its causal correction are estimable, and that a permutation-calibrated screen detects planted order-three leakage with controlled false positives.

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arXiv2026

Human Supervision as an Information Bottleneck: A Unified Theory of Error Floors in Human-Guided Learning

Large language models are trained primarily on human-generated data and feedback, yet they exhibit persistent errors arising from annotation noise, subjective preferences, and the limited expressive bandwidth of natural language. We argue that these limitations reflect structural properties of the supervision channel rather than model scale or optimization. We develop a unified theory showing that whenever the human supervision channel is not sufficient for a latent evaluation target, it acts as an information-reducing channel that induces a strictly positive excess-risk floor for any learner dominated by it. We formalize this Human-Bounded Intelligence limit and show that across six complementary frameworks (operator theory, PAC-Bayes, information theory, causal inference, category theory, and game-theoretic analyses of reinforcement learning from human feedback), non-sufficiency yields strictly positive lower bounds arising from the same structural decomposition into annotation noise, preference distortion, and semantic compression. The theory explains why scaling alone cannot eliminate persistent human-aligned errors and characterizes conditions under which auxiliary non-human signals (e.g., retrieval, program execution, tools) increase effective supervision capacity and collapse the floor by restoring information about the latent target. Experiments on real preference data, synthetic known-target tasks, and externally verifiable benchmarks confirm the predicted structural signatures: human-only supervision exhibits a persistent floor, while sufficiently informative auxiliary channels strictly reduce or eliminate excess error.

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arXiv2026

Admissible Information Structures, Immersion, and the Order of Non-Anticipative Aggregation

This version corrects and supersedes an earlier preprint (arXiv:2601.12541) whose central impossibility theorem was incorrect; the nature of the error and its correction are stated explicitly in Section 1.1. We retain the parts that are valid - the local reduction of pricing to the natural price filtration and its stability properties - and we replace the erroneous global non-existence claim with the statement that is actually true. Two facts are established. First, when the information structure is treated as an admissible (immersion-preserving) enlargement, local martingale pricing reduces to the natural price filtration, and this reduction is stable under restriction and under aggregation when a common pricing measure exists. Second, non-anticipativity of information does not aggregate: there exist signals, each individually and pairwise non-anticipative with respect to the reference Brownian filtration, whose joint observation reveals a function of a future increment; the failure first occurs at order three and is invisible to every lower-order test. We show that this aggregation failure requires dependence among the signals (a masking relation), not independence, and that it is an obstruction at the level of information admissibility (immersion), not at the level of no-arbitrage: the enlarged market continues to admit a local martingale deflator. We situate the results relative to the filtration-reduction program of Grigorian and Jarrow and relate the admissibility notion to predictive (Granger) and interventionist (Pearl) causality.

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arXiv2026

Order-Constrained Spectral Causality for Multivariate Time Series

We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, summarized through orthogonally invariant spectral functionals. We show that the resulting supremum--infimum dispersion functional is the unique diagnostic within this class satisfying order consistency, orthogonal invariance, Loewner monotonicity, second-order sufficiency, and continuity, and that classical Granger causality, directed coherence, and Geweke frequency-domain causality arise as special cases under appropriate restrictions. An information-theoretic impossibility result establishes that entrywise-stable edge-based tests require quadratic sample size scaling in distributed (non-sparse) regimes, whereas spectral tests detect at the optimal linear scale. We establish uniform consistency and valid shift-based randomization inference under weak dependence. Simulations confirm correct size and strong power across distributed and nonlinear alternatives, and an empirical application illustrates system-level directional causal structure in financial markets.

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arXiv2025

Causal PDE-Control Models for Dynamic Portfolio Optimization with Latent Drivers

Classical portfolio models degrade under structural breaks, whereas flexible machine-learning allocation methods often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that integrates structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust and transparent allocation rules under partial information. We construct driver-conditional risk-neutral measures on the observable filtration via filtering together with the corresponding martingale representation, linking pricing, hedging, and portfolio choice under a common information set. We further establish a projection-divergence duality showing that restricting portfolios to the causal driver span selects the feasible allocation closest to the unconstrained optimum under a convex divergence, thereby quantifying the stability cost of deviations from the causal manifold, and derive a causal completeness condition identifying when a finite driver span captures systematic premia. Markowitz, CAPM/APT, and Black-Litterman arise as limiting cases, while reinforcement learning and deep hedging appear as unconstrained approximations within the same pricing-control geometry. Empirically, on a U.S.equity panel with more than 300 candidate drivers, CPCM solvers achieve higher Sharpe ratios, lower turnover, and more persistent premia than econometric and machine-learning benchmarks.

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arXiv2025

Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity

Existing approaches to predictive uncertainty rely either on multi-hypothesis prediction, which promotes diversity but lacks principled aggregation, or on ensemble learning, which improves accuracy but rarely captures the structured ambiguity. This implicitly means that a unified framework consistent with the loss geometry remains absent. The Structured Basis Function Network addresses this gap by linking multi-hypothesis prediction and ensembling through centroidal aggregation induced by Bregman divergences. The formulation applies across regression and classification by aligning predictions with the geometry of the loss, and supports both a closed-form least-squares estimator and a gradient-based procedure for general objectives. A tunable diversity mechanism provides parametric control of the bias-variance-diversity trade-off, connecting multi-hypothesis generalisation with loss-aware ensemble aggregation. Experiments validate this relation and use the mechanism to study the complexity-capacity-diversity trade-off across datasets of increasing difficulty with deep-learning predictors.

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arXiv2025

Is Causality Necessary for Efficient Portfolios? A Computational Perspective on Predictive Validity and Model Misspecification

Portfolio optimization is increasingly argued to require causally identified return predictors to avoid signal inversion and optimization failure. This paper re-examines this claim by studying when predictive signals yield viable efficient frontiers, even under structural misspecification. We show that causal identification is not necessary for portfolio efficiency within static mean--variance and closely related quadratic portfolio optimization frameworks. Instead, efficiency is governed by geometric sufficiency conditions on predictive signals: directional alignment, ranking preservation, and calibration. We formally decompose portfolio efficiency into these three components and show that miscalibration alone attenuates Sharpe ratios even when alignment and ranking are preserved. Robustness is characterized as smooth degradation rather than collapse, with explicit attenuation behavior and continuity of performance under increasing misspecification. The theoretical results are supported by simulations and empirical analysis. Empirical validation combines equity-based illustrations with a large global bond universe spanning multiple currencies, countries, sectors, maturities along the term structure, seniority classes, and credit ratings, together with high-dimensional stress tests, nonlinear data-generating processes, rolling-window analyses, covariance regularization, realistic portfolio constraints, and bootstrap-based statistical validation. Across these settings, optimization geometry remains well-behaved whenever directional alignment is preserved. The results clarify the boundary between causality and portfolio optimization: causality may inform signal representation, but portfolio efficiency at the optimization stage is a geometric property conditional on a given representation.

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arXiv2025

Causal Portfolio Optimization: Principles and Sensitivity-Based Solutions

Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers of a portfolio in terms of its diversification dynamics. The proof relies on the Reichenbach Common Cause Principle, along with the fact that the sensitivities of portfolio constituents with respect to the common causal drivers are themselves causal. A conformal map preserves idiosyncratic diversification from the unconditional setting while optimizing systematic diversification on an embedded space of these sensitivities. Causal methodologies for combinatorial driver selection are presented, such as the use of Bayesian networks and correlation-based algorithms from Reichenbach's principle. Limitations of linear models in capturing causality are discussed, and included for completeness alongside more advanced models such as neural networks. Portfolio optimization methods are presented that map risk from the sensitivity space to other risk measures of interest. Finally, the work introduces a novel risk management framework based on Common Causal Manifolds, including both theoretical development and experimental validation. The sensitivity space is predicted along the common causal manifold, which is modeled as a causal time system. Sensitivities are forecasted using SDEs calibrated to data previously extracted from neural networks to move along the manifold via its tangent bundles. An optimization method is then proposed that accumulates information across future predicted tangent bundles on the common causal time system manifold. It aggregates sensitivity-based distance metrics along the trajectory to build a comprehensive sensitivity distance matrix. This matrix enables trajectory-wide optimal diversification, taking into account future dynamics.

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arXiv2025

Multi-Hypothesis Prediction for Portfolio Optimization: A Structured Ensemble Learning Approach to Risk Diversification

This work proposes a unified framework for portfolio allocation, covering both asset selection and optimization, based on a multiple-hypothesis predict-then-optimize approach. The portfolio is modeled as a structured ensemble, where each predictor corresponds to a specific asset or hypothesis. Structured ensembles formally link predictors' diversity, captured via ensemble loss decomposition, to out-of-sample risk diversification. A structured data set of predictor output is constructed with a parametric diversity control, which influences both the training process and the diversification outcomes. This data set is used as input for a supervised ensemble model, the target portfolio of which must align with the ensemble combiner rule implied by the loss. For squared loss, the arithmetic mean applies, yielding the equal-weighted portfolio as the optimal target. For asset selection, a novel method is introduced which prioritizes assets from more diverse predictor sets, even at the expense of lower average predicted returns, through a diversity-quality trade-off. This form of diversity is applied before the portfolio optimization stage and is compatible with a wide range of allocation techniques. Experiments conducted on the full S&P 500 universe and a data set of 1.300 global bonds of various types over more than two decades validate the theoretical framework. Results show that both sources of diversity effectively extend the boundaries of achievable portfolio diversification, delivering strong performance across both one-step and multi-step allocation tasks.

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arXiv2024

A Portfolio's Common Causal Conditional Risk-neutral PDE

Portfolio's optimal drivers for diversification are common causes of the constituents' correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair constituent-common driver joint distribution modelled by Gaussian copulas. A conditional risk-neutral PDE is obtained for this conditional probability as a system of copulas' PDEs, allowing for dynamical risk management of a portfolio as shown in the experiments. Implied conditional portfolio volatilities and implied weights are new risk metrics that can be dynamically monitored from the PDEs or obtained from their solution.

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arXiv2023

Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction

Multi-modal problems can be effectively addressed using multiple hypothesis frameworks, but integrating these frameworks into learning models poses significant challenges. This paper introduces a Structured Radial Basis Function Network (s-RBFN) as an ensemble of multiple hypothesis predictors for regression. During the training of the predictors, first the centroidal Voronoi tessellations are formed based on their losses and the true labels, representing geometrically the set of multiple hypotheses. Then, the trained predictors are used to compute a structured dataset with their predictions, including centers and scales for the basis functions. A radial basis function network, with each basis function focused on a particular hypothesis, is subsequently trained using this structured dataset for multiple hypotheses prediction. The s-RBFN is designed to train efficiently while controlling diversity in ensemble learning parametrically. The least-squares approach for training the structured ensemble model provides a closed-form solution for multiple hypotheses and structured predictions. During the formation of the structured dataset, a parameter is employed to avoid mode collapse by controlling tessellation shapes. This parameter provides a mechanism to balance diversity and generalization performance for the s-RBFN. The empirical validation on two multivariate prediction datasets-air quality and energy appliance predictions-demonstrates the superior generalization performance and computational efficiency of the structured ensemble model compared to other models and their single-hypothesis counterparts.

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arXiv2023

A causal interactions indicator between two time series using extreme variations in the first eigenvalue of lagged correlation matrices

This paper presents a method to identify causal interactions between two time series. The largest eigenvalue follows a Tracy-Widom distribution, derived from a Coulomb gas model. This defines causal interactions as the pushing and pulling of the gas, measurable by the variability of the largest eigenvalue's explanatory power. The hypothesis that this setup applies to time series interactions was validated, with causality inferred from time lags. The standard deviation of the largest eigenvalue's explanatory power in lagged correlation matrices indicated the probability of causal interaction between time series. Contrasting with traditional methods that rely on forecasting or window-based parametric controls, this approach offers a novel definition of causality based on dynamic monitoring of tail events. Experimental validation with controlled trials and historical data shows that this method outperforms Granger's causality test in detecting structural changes in time series. Applications to stock returns and financial market data show the indicator's predictive capabilities regarding average stock return and realized volatility. Further validation with brokerage data confirms its effectiveness in inferring causal relationships in liquidity flows, highlighting its potential for market and liquidity risk management.

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