arXiv subjects

Miquel Noguer i Alonso

Publications and source records attributed to Miquel Noguer i Alonso.

17 recordsLinked to original sources

arXiv2026

Finding Icebergs in Language-Model Workflow: Diagnosing Latent Structural Fragility with Stochastic Semantic Evidence Graphs

AI-workflow governance cannot be reduced to checking the final answer: an apparently safe answer may rest on a fragile evidence path that ordinary evaluation cannot see, localize or govern. We call this hidden fragility a "structural iceberg": hallucinations and unsupported claims may form its visible tip, while consequential weakness remains submerged. Stochastic semantic evidence graphs (SSEGs) expose these icebergs by preserving workflow channels, propagating local uncertainty and identifying the hidden paths on which an apparently safe output depends. ALCE and RAGTruth show that visible failures at the tip -unsupported citations and hallucinated spans -rest on distinct submerged weaknesses and therefore require different interventions. Across retrieval, tool-use and controlled stress tests, SSEG localizes those weaknesses, supports targeted repair, produces no false automatic passes in 35,000 known-truth cases and reduces ToolSandbox review by 28.8% across 96 executions from two agent models. The same structural view carries into end-to-end governance: in a separately sealed 1,200-case FinGovBench study, adding SSEG to GPT-OSS-20B reduces unsafe releases from 452/660 to 8/660 while releasing all 540 safe cases and correctly distinguishing 592/600 matched workflow pairs. An unchanged-gate transfer to Qwen3-8B releases all 540 safe cases and none of 660 unsafe cases, whereas flat-UQ releases 520 unsafe cases. SSEG therefore moves governance below surface-level output checking, turning hidden evidence dependencies into auditable, path-specific decisions about intervention, revalidation and release.

cs.CL↗

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.

q-fin.PM↗

arXiv2026

The Mathematics of Volatility Surfaces

This paper develops a unified mathematical theory of implied, local, and learned volatility surfaces. Total variance $w_t(k,τ)=τσ_t^2(k,τ)$ is an infinite-dimensional state constrained by positivity, calendar monotonicity, and the butterfly differential inequality. We establish the topology and tangent geometry of this arbitrage set and prove that a nondegenerate Gaussian shock at an active constraint exits with probability tending to one half. Exact invariance therefore requires tangency, reflection, or confinement to an arbitrage-free manifold. We separate this static invariance problem from dynamic no-arbitrage, derive the Musiela maturity-transport identity, and identify the additional fixed-contract martingale restriction. We formulate Hilbert-space dynamics, prove an exact modal reduction with closed-form truncation error, derive Karhunen--Loève factors, identify the portfolio derivative as a vega field, and obtain the covariance-optimal hedge $α^\ast=(H^\ast C H)^{-1}H^\ast Cν$. The local-volatility chart completes the geometry: Dupire local variance is the ratio $a=\partial_τw/g[w]$ of the calendar and butterfly constraint functionals. Neural operators provide arbitrage-free universal approximation through simplex and cone heads. Normalizing-flow maps then add tractable conditional densities: we derive exact change-of-variables formulae for exponential local-variance flows and invertible stick-breaking price-simplex flows, while stating the quasi-invariance conditions required in genuine function space. Finally, fading-signature fields encode surface history and yield autonomous finite-dimensional controlled dynamics. The result is one framework for representation, dynamics, arbitrage, dimension reduction, likelihood-based learning, simulation, and hedging, together with a falsifiable empirical protocol.

q-fin.MF↗

arXiv2026

Path Portfolio Optimization: Defect, Lift, and the Price of Path Complexity

This paper builds Path Portfolio Optimization: portfolio theory on a path-first framework in which the signature is the universal coordinate of the price path, and asks whether it survives estimation. A portfolio is a linear functional of the signature, so the control lives in a truncated tensor algebra, the covariance of signature coordinates is the non-group-like part of the expected signature --- a defect form --- and the whole mean--variance problem becomes a linear system in one tensor. Two structural results follow. The lift is the execution convention: the gap between the Marcus and forward lifts, contracted with portfolio weights, is Fernholz's excess growth rate exactly, so excess growth is the geometricity defect of the portfolio map. And the antisymmetric block at level two is lift-invariant pathwise, so directional signals are convention-free while variance signals and ruin are not. The empirical finding is a dimensional trade-off. With the expected signature known, quadratic path functionals raise the certainty equivalent elevenfold for a pair of assets and sixtyfold for a cross section of twenty; with it estimated, the unregularized policy is severely negative until the sample exceeds roughly six observations per parameter, and shrinkage flips from harmful in the pair to indispensable in the cross section. The entire gain sits in the symmetric block, which is convexity in the terminal increment rather than path-dependence; the path-dependent antisymmetric block earns nothing when the driver has no expected area. And the sample-size floor belongs to unstructured estimation rather than to path complexity: an estimator that fits only the generator of the driver and rebuilds the expected signature recovers almost all of the attainable value at barely one observation per parameter

q-fin.PM↗

arXiv2026

Financial Epiplexity: A Theory of Learnable Market Structure under Bounded Computation

Financial markets are hard to predict, not because price moves are purely random, but because structure is strategic, capacity-constrained, and computationally difficult. Classical information theory measures uncertainty, dependence, and directed flow through entropy, KL divergence, NMI, and transfer entropy. This paper extends that foundation to ask: how much detected structure can a bounded investor learn and reuse? We introduce financial epiplexity: a time-bounded MDL measure of learnable market structure relative to a filtration, representation, model class, and budget. The alpha-relevant object is not raw complexity, but target-specific net compression gain beyond a benchmark, penalizing the model for its description length. This framing aligns with the P-Q wedge: risk-neutral martingality closes arbitrage under a pricing measure, while epiplexity concerns real-world learnability. We prove equal entropy need not imply equal epiplexity, derive finite-sample thresholds for useful regimes, and formalize representation dependence and compute nonmonotonicity. Using the Kelly-Cover-Barron-Cover correspondence, we bound cumulative excess log-growth, Sharpe ratios, sustainable ICs, and breadth by structural bits per period, treating leverage and survival as capacity constraints. The dynamic theory models alpha decay as the migration of private bits into the market budget, crowding as mutual compressibility, and capacity as bit leakage. Finally, the strategic layer explores budget choice, signal congestion, endogenous computational depth, and Red Queen compute competition.

q-fin.MF↗

arXiv2026

A General Theory of Paths: Signatures, Jump Lifts, and Expected Signatures of Self-Exciting Processes

This paper develops a path-first theory using the signature as a universal coordinate for deterministic paths, rough paths, jump streams, and path-valued random variables. Geometricity is presented as a first-order algebraic property with second-order obstructions: a bracket for non-geometric lifts, and a covariance when averaging random paths. This framework links the shuffle identity, Marcus-Ito distinction, expected signatures, signature kernels, and free nilpotent group geometry. We offer four main contributions. (1) The Geometricity-Defect Theorem identifies quadratic covariation and coordinate covariance as the canonical failures of shuffle multiplicativity. (2) The Hopf Square proves that for pure-jump finite-variation paths, the forward Ito signature equals the iterated-sums signature, while the Marcus signature is Hoffman's exponential image of it. (3) Affine and exponential Hawkes processes are shown to admit finite-dimensional linear closures for truncated expected signatures after state-weight augmentation. For scalar Hawkes clocks, this allows explicit identification of baseline, excitation, and decay parameters. (4) An antisymmetric second-level cross-area is proved to detect two-channel Hawkes excitation direction to first order. Secondary results cover kernel-MMD decompositions, free nilpotent truncations, stable-law thresholds, heavy-tail normalizations, and a large-deviation principle. All identities and formulas are validated by a reproducibility script.

math.PR↗

arXiv2026

The Mathematics of Modeling the Future

Modeling the future requires specifying conditional laws relative to an evolving information flow and describing their movement across time. This paper provides a unified mathematical synthesis of this problem along a single spine. Filtrations encode known data; conditional expectation and regular conditional probabilities yield point and distributional forecasts; Markov kernels and semigroups propagate observables and laws; and infinitesimal generators encode local dynamics, producing Kolmogorov equations and stochastic differential equations. Along this spine, martingales isolate surprise, filtering handles partial observation, finance prices futures, stochastic control optimizes choices, and ergodic theory describes the far future. The contribution is architectural. We explicitly connect derivations that turn classical objects into a unified forecasting calculus: the tower property becomes the semigroup law; Ito's formula yields the backward equation after conditioning; integration by parts provides the forward operator; and generator perturbations become model-risk distortions. Forecasting is shown not as mere data extrapolation, but the construction of dynamically coherent conditional distributions constrained by information, geometry, and admissible models. These concepts are illustrated via Gaussian Ornstein--Uhlenbeck and non-Gaussian Cox--Ingersoll--Ross processes, demonstrating how abstract machinery produces explicit transition laws, spectral decompositions, term-structure formulae, and asymptotics in diverse geometries. We recast density evolution as a Wasserstein gradient flow, place forecasting within Hilbert, Fisher--Rao, and Wasserstein geometries, provide a discrete-time empirical dictionary, and address model-risk. The result is a compact mathematical map from information to prediction, local dynamics to global laws, and idealized models to empirical forecasting.

q-fin.MF↗

arXiv2026

The Mathematics of AI Winters: The mathematical Taxonomy of Paradigm Fragility in AI Winter

Two major periods of reduced funding and confidence in artificial intelligence research, commonly called the first and second AI winters, are usually explained through engineering failure, commercial disappointment, and inflated expectations. This article develops a complementary thesis: that the dominant paradigms of those periods also met genuine formal barriers, including limitations of representation, optimisation, computational complexity, statistical learnability, and high-dimensional approximation. The contribution is synthetic rather than archival. We do not claim that particular theorems mechanically caused the winters; rather, we show that several central disappointments of early AI were aligned with mathematically precise bottlenecks. We analyse these bottlenecks through the perceptron impossibility results of Minsky and Papert, the complexity-theoretic hardness of exact neural-network training established by Blum and Rivest, minimax rates for nonparametric estimation in high dimension due to Stone, vanishing-gradient analyses by Hochreiter and by Bengio and collaborators, and classical statistical learning theory in the tradition of Vapnik and Chervonenkis, Valiant, and Blumer and collaborators. We then relate these barriers to the later breakthroughs that mitigated, rather than eliminated, them.

cs.LG↗

arXiv2026

The Mathematics of Heuristic Portfolio Optimization (HPO)

Practitioners allocate capital with forecast-light rules such as equal weight, inverse volatility, risk parity, HRP, and return-adjusted HRP (RA-HRP). This paper develops \emph{Heuristic Portfolio Optimization} (HPO): an information-restricted projection of the Markowitz/tangency solution onto a stable rule class. The implied-return principle, $\mathbf{w}$ is maximum-Sharpe iff $\mathbfμ_e \propto \mathbfΣ\mathbf{w}$, gives closed-form optimality sets for leading heuristics and exposes the Schur-complement substitutions behind HRP. For RA-HRP, we introduce fixed-tree cluster-Sharpe recursion, unit-free HRP--RA-HRP interpolation, tangency conditions, conditional-risk splits, and pathwise/KL decompositions of weight distortion. First-order Sharpe calculus expresses the marginal value of return information as nodewise alphas against HRP and yields a linear KL trust budget. We formalize generic HPO maps, define the implied-return defect, prove that it equals squared Sharpe inefficiency, characterize tree-HPO coincidence by nodewise mass ratios, and give a bias--variance decomposition for estimated rules. Finally, HPO is embedded into Reinforcement Learning Portfolio Optimization (RLPO): every HPO map induces a deterministic stationary policy; static HPO is the $γ=0$ no-friction face of the Bellman problem; RA-HRP supplies a hierarchical policy prior; and dynamic improvement is warranted when continuation value exceeds myopic HPO defect plus frictions. A performance-difference identity prices the myopic value gap, gives an $\varepsilon/(1-γ)$ myopia bound, and identifies nodewise alphas as policy-gradient coordinates of the hierarchical actor. Thus HPO is the static optimality layer and RLPO the dynamic control layer. The conditions are GRS-testable, extend to mean--CVaR and expected utility under ellipticity, and become Kelly-growth conditions in diffusion limits.

q-fin.PM↗

arXiv2026

Markets Are Not Random, They Are Hard to Predict

Financial returns are often called ``random,'' but the word conflates ontic chance, epistemic ignorance, strategic feedback, and model instability. This essay argues that financial markets are not random in the ontic sense in which a quantum measurement is random. They are causal economic systems whose future is hard to predict because relevant causes are hidden, costly to observe, strategically used, capacity constrained, and sometimes governed by a changing law. The formal language of finance already encodes this distinction. Prices live on filtered probability spaces because agents have partial information; derivatives are priced under a risk-neutral measure $\Q\ne\Prob$ because pricing is an instrumental change of measure rather than a statement about the real data-generating law; and no-arbitrage gives martingality under an equivalent pricing measure, not full predictability failure under every real-world information set. The paper separates no-arbitrage, informational efficiency, and net exploitability; uses the Doob decomposition to isolate risk-compensated predictable drift from martingale innovation; adds a capacity-and-survival layer explaining why positive signals need not be scalable; relates the $\Prob$--$\Q$ wedge to stochastic-discount-factor geometry and relative entropy; formalises filtration sufficiency, model-selection landscape risk, and intervention-stable causality; and connects reflexivity, microstructure, and Knightian ambiguity to a unified entropy ledger. The disciplined thesis is therefore not that markets are unknowable, nor that they are literally random. Markets are hard to predict, and hardest exactly where prediction is costly, competitive, self-defeating, capacity limited, or invalidated by regime change.

q-fin.MF↗

arXiv2026

Anticipatory Portfolio Optimization

A portfolio is \emph{anticipatory} when its optimizer acts on a richer model than the myopic, price-taking estimator used to calibrate it. Enrichment may be informational, via enlarged filtrations; dynamic, via horizon forecasts; or performative, via the deployment law induced by market impact. We give a decision-theoretic definition for all three cases and measure anticipation by the realized control gap between enriched controller and restricted estimator. The same quadratic geometry separates information, planning value, impact correction, and overfitting. For log utility under initial enlargement, value is the information-drift energy $\frac12\mathbb{E} \int_0^Tα_t^2\,dt$, equivalently mutual information or relative entropy. In mean-variance form, signal value is $\frac{1}{2γ}{\rm tr}(Σ^{-1}Ω)$. Dynamic forecast anticipation gives a finite-horizon quadratic premium in the forecast stack, while permanent impact changes the price-taking allocation $θ_{\rm na} =(Λ+γΣ)^{-1}μ$ into $θ_{\rm an} = (2Λ+γΣ)^{-1}μ$ and reveals a spectral phase transition for naive recalibration. The main result is a stacked finite-horizon LQG decomposition: information, forecast, and impact combine into an information trace plus one inverse-precision norm, whose expansion yields the impact term, forecast term, and signed forecast-impact interaction. Sharp angle bounds and an orthogonal nonnegative projection identity resolve the signed term. The stationary extension endogenizes information covariance as Kalman error reduction and carries impact anticipation to an infinite-horizon Lyapunov trace with transaction costs. Finally, the penalty $\frac{1}{2}{\rm tr}(H^{-1}Σ_\varepsilon)$ shows that correctly specified anticipation creates value, vacuous anticipation has zero value, and misspecified anticipation is harmful when estimated structure is optimized as true.

q-fin.PM↗

arXiv2026

Distributional Portfolio Optimization (DPO): A Unified Framework for Distributions over Weights, Returns, and Parameters

Classical portfolio optimization treats expected returns, covariances, and allocations as deterministic. Modern practice replaces at least one by a distribution: a posterior over parameters, a law of future returns, a stochastic allocation policy, or a distributional-robustness set. We call distributional portfolio optimization (DPO) the unified framework in which weights, returns, and parameters are all modeled as probability measures, organized around the joint coupling Gamma_theta(dw,dr) and its marginal triple (W,R,P). The contribution is synthetic and structural: we organize Bayesian, robust, chance-constrained, stochastic-allocation, and distributional reinforcement-learning portfolio methods through this coupling and prove boundary results connecting them, including a portfolio specialization of Wasserstein-CVaR duality, a static no-randomization theorem, a Bayesian credible-radius calibration of Wasserstein DRO, a Gaussian-isotropic second-order conservatism bound, a conditional two-sided rate W_1 = Theta(n^{-(1+alpha)/2}) governed by the local boundary Holder exponent alpha in [0,1], and a risk-shifted distributional Bellman contraction. A controlled experiment shows that across factor models at K in {10,25,50}, the credible-radius rule lands within 3-7 bp of the oracle out-of-sample tail risk and beats a 24-month validation-tuned radius while spending no validation data. On a K=25 DJIA backtest, equal-weight, no-view Black-Litterman, and Ledoit-Wolf shrinkage attain higher Sharpe than every distributional method; the operational claim is therefore confined to calibration-without-validation and turnover, not raw-return dominance.

q-fin.PM↗

arXiv2026

A Unified Theory of Ownership Concentration, Overlap, and Dependence

Ownership concentration is not a scalar. For a normalized investor-stock matrix $A$, it has three irreducible layers: concentration across investors, concentration across stocks, and dependence in the joint assignment of investors to stocks. This paper develops a unified quadratic framework for those layers and shows that the same residual operator that measures static overlap also governs linearized market transmission. Raw micro concentration $M(A) = \sum_{i,j} A_{ij}^2$ admits exact row and column decompositions, support bounds, and fixed-marginal extremal characterizations on the transportation polytope. Benchmark-adjusted dependence $\mathcal{X}(A) = \sum_{i,j} (A_{ij} - p_i s_j)^2 / (p_i s_j)$ admits two exact decompositions: it is a size-weighted average of investor-level deviations from the market portfolio and, symmetrically, of stock-level deviations from the investor base. The paper also proves a multiscale aggregation law: under any partition of investors, total dependence splits exactly into between-group dependence and within-group heterogeneity. Spectrally, $\mathcal{X}(A)$ equals the sum of squared nontrivial singular values of the whitened matrix $D_p^{-1/2} A D_s^{-1/2}$. The residual operator $L$ then yields two dynamic consequences: idiosyncratic fire-sale vulnerability is bounded by the dominant overlap mode $ρ(A)$, while aggregate benchmark-relative alpha variance has worst-case capacity $ρ(A)^2$ and isotropic average-case capacity $\mathcal{X}(A)$. The fixed-marginal geometry also motivates a feasible-range sparsity score that benchmarks observed micro concentration against the sharp minimum and maximum implied by the marginals. The resulting framework separates scale concentration, feasible sparsity, overlap, and linear transmission in a way that is mathematically transparent and empirically usable for work on crowding, fragility, and systemic risk.

q-fin.PM↗

arXiv2025

Financial Information Theory

This paper introduces a comprehensive framework for Financial Information Theory by applying information-theoretic concepts such as entropy, Kullback-Leibler divergence, mutual information, normalized mutual information, and transfer entropy to financial time series. We systematically derive these measures with complete mathematical proofs, establish their theoretical properties, and propose practical algorithms for estimation. Using S&P 500 data from 2000 to 2025, we demonstrate empirical usefulness for regime detection, market efficiency testing, and portfolio construction. We show that normalized mutual information (NMI) behaves as a powerful, bounded, and interpretable measure of temporal dependence, highlighting periods of structural change such as the 2008 financial crisis and the COVID-19 shock. Our entropy-adjusted Value at Risk, information-theoretic diversification criterion, and NMI-based market efficiency test provide actionable tools for risk management and asset allocation. We interpret NMI as a quantitative diagnostic of the Efficient Market Hypothesis and demonstrate that information-theoretic methods offer superior regime detection compared to traditional autocorrelation- or volatility-based approaches. All theoretical results include rigorous proofs, and empirical findings are validated across multiple market regimes spanning 25 years of daily returns.

q-fin.PM↗

arXiv2024

Game Theory and Multi-Agent Reinforcement Learning : From Nash Equilibria to Evolutionary Dynamics

This paper explores advanced topics in complex multi-agent systems building upon our previous work. We examine four fundamental challenges in Multi-Agent Reinforcement Learning (MARL): non-stationarity, partial observability, scalability with large agent populations, and decentralized learning. The paper provides mathematical formulations and analysis of recent algorithmic advancements designed to address these challenges, with a particular focus on their integration with game-theoretic concepts. We investigate how Nash equilibria, evolutionary game theory, correlated equilibrium, and adversarial dynamics can be effectively incorporated into MARL algorithms to improve learning outcomes. Through this comprehensive analysis, we demonstrate how the synthesis of game theory and MARL can enhance the robustness and effectiveness of multi-agent systems in complex, dynamic environments.

cs.MA↗

arXiv2021

FinEAS: Financial Embedding Analysis of Sentiment

We introduce a new language representation model in finance called Financial Embedding Analysis of Sentiment (FinEAS). In financial markets, news and investor sentiment are significant drivers of security prices. Thus, leveraging the capabilities of modern NLP approaches for financial sentiment analysis is a crucial component in identifying patterns and trends that are useful for market participants and regulators. In recent years, methods that use transfer learning from large Transformer-based language models like BERT, have achieved state-of-the-art results in text classification tasks, including sentiment analysis using labelled datasets. Researchers have quickly adopted these approaches to financial texts, but best practices in this domain are not well-established. In this work, we propose a new model for financial sentiment analysis based on supervised fine-tuned sentence embeddings from a standard BERT model. We demonstrate our approach achieves significant improvements in comparison to vanilla BERT, LSTM, and FinBERT, a financial domain specific BERT.

cs.CL↗

arXiv2020

Deep Reinforcement Learning for Asset Allocation in US Equities

Reinforcement learning is a machine learning approach concerned with solving dynamic optimization problems in an almost model-free way by maximizing a reward function in state and action spaces. This property makes it an exciting area of research for financial problems. Asset allocation, where the goal is to obtain the weights of the assets that maximize the rewards in a given state of the market considering risk and transaction costs, is a problem easily framed using a reinforcement learning framework. It is first a prediction problem for expected returns and covariance matrix and then an optimization problem for returns, risk, and market impact. Investors and financial researchers have been working with approaches like mean-variance optimization, minimum variance, risk parity, and equally weighted and several methods to make expected returns and covariance matrices' predictions more robust. This paper demonstrates the application of reinforcement learning to create a financial model-free solution to the asset allocation problem, learning to solve the problem using time series and deep neural networks. We demonstrate this on daily data for the top 24 stocks in the US equities universe with daily rebalancing. We use a deep reinforcement model on US stocks using different architectures. We use Long Short Term Memory networks, Convolutional Neural Networks, and Recurrent Neural Networks and compare them with more traditional portfolio management. The Deep Reinforcement Learning approach shows better results than traditional approaches using a simple reward function and only being given the time series of stocks. In Finance, no training to test error generalization results come guaranteed. We can say that the modeling framework can deal with time series prediction and asset allocation, including transaction costs.

q-fin.PM↗