arXiv subjects

Alejandro Rodriguez Dominguez

Publications and source records attributed to Alejandro Rodriguez Dominguez.

At least 19 recordsLinked to original sources

arXiv2026

Admissible Portfolio Optimization: Information Constraints, Conditional Efficient Frontiers and the Price of Causal Identification

Mean--variance portfolio choice takes the conditioning information as given, so that two errors about it, using variables not available at the decision time and treating common variation as idiosyncratic, pass into the portfolio unseen. This paper turns what that practice assumes into a condition declared before estimation, certified from data and priced when it fails. The conditioning information becomes a decision variable subject to admissibility constraints on availability, arbitrage, statistical separation and, for interventional claims, invariance across regimes; an order in which no risk--return quantity enters selects an information class, and the classical problem is solved inside it. We prove that solutions exist, that the value of information is monotone only under an embedding that portfolio constraints can break, so that selection by decision loss admits look-ahead information whenever offered, that the two-stage solution and the joint envelope are minimal elements of two orders on one set, that the diversifiable part of risk is a property of the admissible class, and that causal identification has an explicit price. Allocation performance is downstream of the framework, since the information decision enters the decision regret at second order and the reported risk at first order, while the weights themselves move at first order. On market data the condition holds on small sets of individual securities and fails on pre-diversified portfolios and on books of realistic size, where a factor model with diagonal residual understates its portfolio's variance by a factor that the consequence statistic announces in advance; selecting the same information by decision loss yields portfolios that promise a fraction of the risk they realize.

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arXiv2026

Teacher-Anchored Selection of Post-Training Quantized Models under Domain Shift

Compressing a trained model yields a family of deployment candidates, and under domain shift the most compressed one need not be the one to deploy. We study selection over such a family, with candidates and teacher fixed and target labels absent or scarce. Two findings organize the label-free case. Minimum teacher distortion behaves almost as a constant rule, selecting the same eight-bit, per-channel, unclipped configuration in every run, which does not minimize empirical target cross-entropy. Established estimators divide sharply: in the overconfident-collapse regime of the CNN families, confidence-based estimators order the family close to backwards, and the diagnostics that identify it need the labels the setting denies, while output-distribution estimators match the teacher-relative anchor and on one architecture beat it. Distortion is nonetheless stable, so a supervised term can move selection away from it. Combining the two, we give exact quadratic identities for a canonical quadratic analogue of the family. We also show that under symmetric corruption the label-dependent part of a criterion linear in the label indicator is multiplied by one common factor whenever its coefficient sums are candidate-invariant, a class holding teacher contrasts and accuracy but not cross-entropy. These characterize the score's components without bounding selection regret. Across one hundred and thirty-four candidate families, one per independently trained convolutional or Vision Transformer teacher, anchoring reduces mean regret at the smallest label budget in every setting, an advantage that fades beyond twenty-five labels.

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arXiv2026

Causal Price-of-Risk Mandates under Overlapping Information

We study whether causal risk mandates constructed from overlapping information blocks can be implemented by one self-financing portfolio that is optimal under pooled information. In an incomplete continuous Brownian market, signal-responsive exposures are projected onto traded Brownian directions and embedded as closed subspaces of a predictable Hilbert space. Each causal mandate is the attainable projection of an identified, baseline-centered intervention surface and is therefore fixed upstream of the allocator. A first exact decomposition separates non-traded structural response, incompatibility across local mandates, and distortion of the common traded book. A fusion operator corrects duplication of common risk directions. The main theorem shows that exact causal decentralization holds if and only if the pooled enlargement preserves reference martingales, the pooled optimum has no component outside the additive desk span, the local causal shadows are compatible with one common book, and that book equals the additive pooled optimum. Under immersion, log-growth regret separates into pooled-interaction loss and common-book distortion, while raw causal implementation error also contains non-attainability and incompatibility. No common benchmark can reduce incompatibility. We derive the unique allocation under a quadratic causal-mandate penalty and exact comparative statics in a two-desk model with shared, desk-specific, and pooled-interaction risk. Additional results cover joint interventions, representation stability, admissible coalitions, and a covariance-weighted continuous-semimartingale formulation. The conclusions are partial-equilibrium statements for continuous markets.

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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

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

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

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

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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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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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.

cs.LG↗

arXiv2026

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

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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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

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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