Papers

Physics-informed neural networks provide a flexible framework for learning parametric PDE solution families without labeled data, yet preserving accurate derivatives across heterogeneous regimes remains challenging. Structured neural solvers offer compact representations, but restrictive conditional parameterizations can limit adaptation across the solution family. We introduce BeTINN, a structured conditional architecture extending time-induced modulation through multi-directional time-parameter conditioning and a joint residual pathway. We evaluate BeTINN on the Heston stochastic-volatility PDE, a demanding parametric problem with mixed derivatives and economically relevant first- and second-order sensitivities. BeTINN improves joint accuracy across normalized option value and key sensitivity metrics relative to our baselines. Controlled ablations characterize the roles of its architectural components. We further find that validation physics loss is informative but does not fully determine differential fidelity, and that accurate solution values can coexist with localized derivative errors. These results support structured conditional adaptation and motivate derivative-aware evaluation when sensitivities are downstream quantities of interest.

We study a local stochastic volatility (LSV) model in which the variance factor follows a generalized Langevin equation (GLE) with colored noise, and past returns act on variance through a memory kernel with state-dependent amplitudes. For kernels given by finite sums of exponentials, we prove existence, uniqueness, and non-explosion under a growth condition linking the volatility map to the potential. In a one-mode family with a polynomial potential, feedback through log returns can cause explosion exactly when the squared volatility factor grows faster than the restoring force. Under structural and nondegeneracy conditions, an exact reduced Markovian state has a smooth density solving a deterministic forward equation. The Dupire conditional expectation therefore requires no stochastic partial differential equation. Under a bounded Sharpe ratio, exponential utility selects the minimal entropy martingale measure, whose premium solves a quadratic backward stochastic differential equation. Under a regularity hypothesis, which we verify in special cases with and without leverage, the premium depends only on the current state, and the squared VIX equals the expected average future local stochastic variance. Finally, a regularized calibration problem with bid–ask constraints admits a minimizer whenever a feasible point has finite objective value.

4Cast Lab is a free, open-source application for machine learning, econometrics and statistical analysis that runs on the user's own computer, with no installation, no programming and no data leaving the machine. It was developed at the E|M|E|F Lab, Department of Economics, Democritus University of Thrace, for researchers, analysts, instructors and students in any field. Its Forecasting mode trains eight learning algorithms (with three kernels for SVM/SVR), implemented from scratch, under leakage-safe validation for time-ordered data; it selects models by cross-validation, compares the selected model with every alternative and with naive benchmarks through formal tests of predictive accuracy, and documents each run in a methods report and a Python script that the user can export. Its Estimation mode covers the core of applied econometrics, from OLS with robust inference to ARIMA, ARDL, VAR/VECM and GARCH. This paper describes the design, the interface and the workflow of version 4.6.2, reports a validation of 1,234 numerical results against statsmodels, linearmodels, arch, scikit-learn and NIST certified values, illustrates the workflow with three examples, and discusses current limitations.

We present a statically and dynamically arbitrage-free European option market model with smooth interpolation between option prices, based on the SANOS framework, and prove that its dynamics admit a unique strong solution. In spirit, it is a stochastic model for local volatility when the latter is used as a representation of a European option price surface, not as a pricing model. We illustrate the strength of our approach on S&P Index Option data from January 2022 to August 2025. We show that the model's initial state fits within bid/ask for more than 95% of relevant market option prices. We then train the model dynamics under $\mathbb{P}$ and $\mathbb{Q}$ and show that the model is indeed free of arbitrage while fitting the dynamics of the market well. We also propose a range of BHW-tests to test for absence of arbitrage.

Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.

A conditional normalizing flow can produce extreme scenarios even when its point forecasts appear reasonable. We compare two fitted models for daily Treasury yield changes at eleven maturities reconstructed from Federal Reserve curve parameters. Both use an LSTM, an auxiliary location head, and an affine residual flow. On a previously unused 60-date window, the frozen Student-t model generated an absolute standardized coordinate of 34.3 million. A Gaussian-base model with tighter coupling scale control reached 14.72. Each generated 600,000 vectors. The original model's scenario-mean MSE was 33,908.95, while its location-head MSE was 0.3376. The stabilized model's two estimates remained close. Across five development windows, the stabilized maximum was 17.33 among three million vectors. Stability did not imply better prediction: historical simulation had better distributional scores and coverage closer to nominal on the new window. The original flow also had a better log score despite its extreme samples. Frozen-model evaluation is reproducible, but the comparison does not isolate architectural effects or establish a general forecasting advantage.

Feature selection is a central problem in high-dimensional financial regression, where large numbers of engineered variables and strong correlations among predictors reduce model stability and interpretability. $L_1$ regularization (Lasso) is widely used for sparse regression, but its shrinkage can be restrictive when informative signals are spread across correlated variables. Exact sparse regression avoids this shrinkage but requires solving a combinatorial optimization problem that is computationally difficult and is typically fit to minimize in-sample rather than out-of-sample error. This paper presents a feature selection framework based on Monte Carlo Tree Search with Generalized Nested Rollout Policy Adaptation (GNRPA). Feature selection is formulated as a sequential decision process, and candidate subsets are scored by their out-of-sample validation performance rather than training error. The method also supports a lexicographic objective accounting for subset size and multicollinearity. We study this approach on a contemporaneous explanatory regression task: explaining the weekly return of the NASDAQ-100 index from 1,072 engineered features spanning market, macroeconomic, and factor data. This isolates the value of subset selection under multicollinearity from the separate problem of predictive forecasting. On this task, the proposed method identifies sparse feature subsets with higher out-of-sample explanatory power than an optimized Lasso baseline, reaching an out-of-sample $R^2$ of 0.6961 versus 0.6313 for Lasso. These results suggest that Monte Carlo Tree Search is a practical alternative to convex regularization for sparse explanatory feature selection in financial regression, with potential value for factor attribution and risk decomposition where transparency matters as much as out-of-sample fit.

I study how intermediary liquidity affects mortgage resolution using 1.9 million Ginnie Mae buyout options from 2019 to 2022. When funding markets froze in 2020, nonbank issuers repurchased far fewer delinquent loans than depositories servicing loans in the same pools and, within the same issuer and month, shifted repurchases away from large balances, the loans that require the most cash. About $19 billion of repurchases were delayed, and most were completed later. A model of rationing by value per dollar of cash explains this pattern and shows that borrower information is most valuable when funding is intermediate.

Expectiles are the only law-invariant risk measures that are both coherent and elicitable. Unlike Conditional Value-at-Risk (CVaR), however, they do not admit a Rockafellar–Uryasev representation that admits tractable Wasserstein reformulations. We address this difficulty by developing an envelope theorem for worst-case expectiles that characterizes the worst-case expectile over a Wasserstein ambiguity set as the unique root of a worst-case expectation with a two-piece affine integrand. This representation permits direct application of standard Wasserstein duality. Using this result, we reformulate a multi-period tri-level mean–expectile portfolio problem as four parametric linear programs with constraints. We establish four structural properties of the proposed model: an endogenously damped price of robustness, a decision-dependent critical radius beyond which the expectile tail component becomes inactive, exact recovery of the nominal model at zero ambiguity, and a characterization of how the Wasserstein ground metric determines whether the limiting portfolio becomes more concentrated or more diversified. Numerical experiments on 90 FTSE constituents over 3,341 out-of-sample trading days show that the expectile model outperforms a CVaR model matched on ambiguity set, radius, ground metric, and trade-off weight in all nine parameter cells—significantly so whenever the radius is non-trivial. The experiments further confirm the predicted degeneracy under the ground metric.

Forecasting resale prices of used electronics is critical for subscription-based platforms where pricing errors translate directly into risk. Unlike structured financial markets, second-hand electronics exhibit high volatility, sparse listing histories, and non-normal price dynamics - yet no systematic time-series benchmark exists for this domain. This paper presents the first multi-horizon benchmark of statistical and deep learning forecasting models for used electronics price prediction. We use a large-scale dataset of daily price listings from Polish online marketplaces (January 2022 to March 2025, 100+ smartphone and laptop models) and evaluate eleven models across six horizons from 1 to 365 days, covering classical methods (ARIMA, ETS, Theta), recurrent and convolutional networks (LSTM, TCN), and modern deep architectures (N-BEATS, N-HiTS, TFT, PatchTST, Informer). Three complementary evaluation protocols assess trajectory fitness, one-shot endpoint accuracy, and cross-horizon transfer. N-BEATS achieves the lowest MAPE beyond 30 days, reaching 8.51% at 365 days versus 14.94% for the best statistical baseline - a 43% reduction. At short horizons (1-7 days), all models converge near 0.72% MAPE and the naive baseline remains competitive. A single N-BEATS model trained at 365 days generalizes to all shorter horizons, eliminating the need for horizon-specific models. N-BEATS and N-HiTS also demonstrate superior hyperparameter stability.

Wavelet-based financial forecasters typically use the transform only to denoise, or reduce it to a single spectral snapshot at the forecast origin, and the convolution that produces the coefficients is usually bilateral, so it can read past the forecast origin. DSTNet instead retains the recent evolution of filter-bank magnitudes as a causal Dynamic Spectral Trajectory, built from seven trailing technical indicators over a twenty-day lookback with a one-sided Morlet-derived filter bank and an explicit burn-in for the left-boundary transient. A factorized Scale-Temporal Spectral Transformer attends along the time and filter-bank axes separately, a learned gate fuses the spectral branch with a CNN-BiLSTM, and horizon-specific gates emit one, three, five, and ten day forecasts in a single pass. We evaluate seven equity indices and gold under a common expanding-window protocol and an untouched one-year hold-out, against nine learned baselines and a random-walk persistence benchmark. Under MAE and MAPE, persistence is the strongest of the ten fixed competitors in 29 of the 32 series-horizon cells and DSTNet is the only model below it in every cell, by 0.7 to 0.9 percent at one day and 3.4 to 4.5 percent at ten days. At one day, paired testing favours DSTNet against the weaker learned baselines but is inconclusive against persistence and the strongest learned forecasters. A downstream allocation diagnostic does not support an equity-timing advantage on any of the seven indices.

Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed baseline weights are chosen to balance sampling uncertainty against temporal drift. Around this reference distribution, the ambiguity set addresses two complementary forms of distributional misspecification by allowing an adversary to reweight the observed trajectories subject to a $\phi$-divergence constraint and perturb their paths subject to an optimal-transport (OT) constraint. We derive a joint first-order expansion in which the leading-order increase over the nominal expected loss decomposes into a reweighting contribution determined by the dispersion of hedging losses across trajectories and a transport contribution determined by the sensitivity of the loss to path perturbations. This expansion yields an explicit finite-dimensional adversarial attack that replaces the distributional inner supremum with a tractable first-order approximation. Across stationary and nonstationary Heston dynamics and a generalized affine diffusion (GAD), the experiments show complementary benefits from reweighting and transport, with joint adversarial training providing the largest gains under nonstationarity.

We develop a posteriori primal-dual bounds for numerical approximations of European option prices in the Uncertain Volatility Model. Given a smooth candidate approximation of the value function, a feedback control induced by its Hessian yields a primal lower bound. On the dual side, we derive a representation based on a matrix-valued Gamma field, which provides an upper bound through a nonnegative Hamiltonian penalty. We further show that, when the dual field is generated by the candidate itself, this upper bound admits an equivalent representation in terms of the residual of the associated Black-Scholes-Barenblatt equation. We then study discrete-time approximations of these primal and dual quantities and quantify the corresponding discretization errors. Finally, we investigate their numerical evaluation for candidates obtained by stochastic policy-gradient and physics-informed neural-network methods, and compare the resulting estimates with a martingale dual approach from the stochastic-control literature. The numerical experiments highlight the importance of derivative accuracy, and in particular of second-order information, for obtaining tight a posteriori bounds.

On-chain transfer volume is often used to describe activity in tokenized real-world assets (RWAs), although recorded transfers may reflect very different economic functions, including token creation, destruction, issuer-related operations, and movements between other addresses. Ownership measures face a similar problem because a large address balance may belong to a pool or intermediary that represents multiple investors. We address these two measurement problems by decomposing transfer activity and making ownership coverage explicit. Transfer turnover is calculated before and after observable event categories are separated, using the same asset, observation window, and supply denominator. For ownership, we compare concentration measured against total supply with concentration among the addresses that remain after identified intermediaries are excluded. Using Ethereum-based tokenized funds from December 2025 to August 2026, we find that transfer classification can materially change measured turnover. We also show that removing an intermediary can lower concentration when measured against total supply while concentration among the remaining addresses increases. Transfer activity and address concentration need to be interpreted with their underlying transaction functions and ownership coverage in mind. These measures provide evidence about liquidity-related activity, but they do not directly measure market liquidity. The code and data used in the analysis are available at https://github.com/atytmr07/rwa-liquidity.

Market-regime models typically assume a finite set of discrete latent states. We examine whether high frequency limit-order-book dynamics exhibit distinct regime separation or apparent regimes result from discretising an underlying continuum, analysing deep limit-order book data for EURO STOXX 50 index futures across 987 clean trading days from 2022 to 2025 using 30, 45 and 60-second aggregation windows. Market states are represented by symmetric positive definite covariance matrices and analysed under Log-Euclidean and affine-invariant geometries; the resulting state cloud has an effective dimension of approximately 1.4. A causal anomaly layer filters statistical, calendar and rollover contamination, while label-free economic validation evaluates market-state separation independently of volatility-based proxy labels. A 17-method zoo spanning conventional and Riemannian representations, reinforced by full-cloud geometric certificates, consistently favours a continuum over a discrete regime structure. A dominant latent coordinate captures between 83.66% and 85.27% of variation in the covariance-state geometry and tracks VSTOXX without regime labels, remaining stable across years although its average level shifts with market conditions, indicating that conventional regimes are coarse quantisations. A divisive hierarchy spanning macro, macro-subregime, micro and micro-subregime tiers is evaluated using expanding-year walk-forward tests, with out-of-sample performance strongest at the macro tier while finer tiers fail to generalise; continuous fine-scale information nonetheless remains predictive, and its discretisation causes the performance loss. Forecasting performance peaks near ten minutes, reaching a maximum pooled R2_OOS of 0.7483. Overall, the latent stress coordinate defines a stable, low-dimensional geometric continuum that captures market stress and its predictive dynamics.

Formulaic alpha discovery seeks symbolic expressions that predict cross-sectional asset returns. In deployment, multiple formulas are combined into an alpha pool, where each formula is valued through the complementary information it contributes to joint predictive performance. While Reinforcement Learning and Generative Flow Networks have emerged as promising paradigms for generating formulaic alphas, existing frameworks face three related challenges. First, generating formulas individually leaves pool context and inter-formula complementarity outside the generative state. Second, formula-wise generation lacks a unified mechanism for preserving and revising structures at different levels. Third, pool-level rewards jointly reflect predictive performance and redundancy but cannot be differentiated directly through symbolic evaluation to train the generator. To overcome these challenges, we introduce AlphaPADI (Formulaic Alpha Discovery via Pool-Aware Hierarchical Discrete Diffusion), a novel framework built around three components: (1) grammar-constrained buffer initialization that constructs syntactically valid pool candidates, (2) pool-aware hierarchical diffusion that reconstructs complete pools at multiple structural scales under the current pool context, and (3) reward-guided pool refinement that evaluates joint predictive performance and inner diversity, updates the elite buffer, and trains the reverse model through reconstruction and preference learning. Empirical results on the Chinese and U.S. stock markets demonstrate that AlphaPADI outperforms the evaluated baselines in both predictive and portfolio performance, thereby validating pool-aware generation as an effective framework for automated alpha discovery.

Deep Research (DR) agents have demonstrated strong capabilities in complex, research-oriented tasks through autonomous planning, iterative retrieval, multi-step reasoning, and structured reporting. However, adapting DR agents to finance introduces unique challenges: financial analysis demands the joint completion of heterogeneous sub-tasks spanning diverse data types, tools, and analytical workflows. We identify three key requirements for a professional financial DR agent: integration of authoritative, heterogeneous financial data sources; specialized analytical tools and skills; and dedicated sub-agents for domain-specific sub-tasks. Building on these principles, we propose FinNextAssist, an end-to-end deep research framework designed for professional financial analysis. FinNextAssist decomposes the research process into four stages: Task Planner, Evidence Compiler, Reasoning Engine, and Report Assembler, and introduces two novel lightweight sub-agents: TabAgent, for cross-market financial table understanding, and HeteroAgent, for cross-modality heterogeneous financial data interpretation. Extensive experiments on FinDeepResearch, the Finance Agent Benchmark, and FinTMMBench-Web show that FinNextAssist substantially outperforms both strong proprietary and open-source DR agents, with ablation studies confirming the contribution of each component across diverse markets and languages.

Neural network-based approaches have emerged as efficient alternatives to traditional optimization-based procedures for the calibration of stochastic volatility models. However, existing work has focused primarily on predictive accuracy, with comparatively little attention devoted to understanding the structure of the learned inverse calibration mappings. In this work, we analyze neural calibration mappings for the Heston and rough Heston models across multilayer perceptron, highway, and softmax-parametrized highway architectures, using complementary Shapley-based methods from explainable AI. Specifically, we consider SHAP and $\nu$SHAP explanations, which capture distinct, complementary notions of feature relevance, corresponding to sensitivity and sufficiency of feature subsets, respectively. Short maturities and smile wings consistently dominate parameter inference, and the dominant attribution structure remains qualitatively stable across architectures despite differences in predictive accuracy and parameter count. Parameter-specific differences between SHAP and $\nu$SHAP further reveal how distinct regions of the implied volatility surface contribute to parameter recovery and expose substantial redundancy in the calibration input. Building on this redundancy, we show that $\nu$SHAP explanations can guide a significant reduction in input dimensionality for the rough Heston model while matching calibration accuracy relative to the full implied volatility surface. These findings demonstrate that complementary Shapley-based methods provide structural insight into learned inverse calibration mappings beyond predictive error metrics, and offer a practical route to feature selection in neural calibration problems.

Short-horizon price-trend prediction from limit order books in equity and intraday electricity markets requires models that combine predictive quality with low single-sample latency and a small serialized model size to keep pace with rapid and continuous market updates. We introduce MBOFormer, a 7,203-parameter causal transformer, and MBOFusion, a 14,371-parameter extension with a slow temporal-context branch. Both models process market-by-order (level-3) histories of individual order submissions, cancellations, and executions. We compare them with level-2-based baselines that process sampled order-book snapshots and simple statistics instead of their underlying messages. Across three markets and four prediction horizons, our models achieve the highest mean macro-F1 in eleven of the twelve settings in a comparison against other benchmark models of varying sizes. Both our models achieve sub-millisecond median inference on a single Apple M2 CPU thread and have serialized state dictionaries below 70 kB. MBOFormer is 5.1x-8.1x faster than the million-parameter baselines at comparable predictive quality. Our results show that fine-grained market event history can reduce the need for model size under tight deployment constraints for short-term equity and electricity price forecasting tasks.

In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price options within these extended models, we derive the corresponding reflected forward-backward stochastic differential equations (RBSDEs) and employ data-driven numerical methods to solve them for both pricing and hedging purposes. The RBSDE framework enables the modelling of the future evolution of the option price. Furthermore, we conduct a convergence analysis of the proposed numerical method and present numerical experiments that illustrate the performance of the extended models, as well as the accuracy and efficiency of the RBSDE-based approach.

European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale construction selects, among all calibrated martingales, the one closest to Bachelier dynamics; it permits fast calibration at discrete maturities and recovers the Dupire local-volatility (LV) model as the maturity grid is refined. This article develops a modular calibration overlay for existing stochastic and path-dependent volatility models. We sequentially construct a martingale that matches all prescribed marginals exactly while remaining as close as possible, in an adapted Knothe-Rosenblatt sense, to the reference dynamics. As with the Bass LV model, each calibration step is amenable to an efficient Martingale Sinkhorn algorithm. We develop the theoretical foundations, numerical implementation and consider convergence to the SLV model. We also benchmark the method for Heston and Bergomi finite-factor path-dependent volatility dynamics and develop the multi-asset extension.

Bank treasury portfolios must balance yield, liquidity, and interest-rate risk across bonds of different maturities. Static allocation rules are ill-suited to this task: portfolios concentrated in long-duration securities with no dynamic adjust- ment mechanism can accumulate large mark-to-market losses and liquidity stress under rising interest rates, as illustrated by the failure of Silicon Valley Bank in 2023. We develop a tractable simulation-based framework for multi-period bond port- folio optimization under interest-rate risk and proportional transaction costs. Yield-curve dynamics are modeled using the Dynamic Nelson-Siegel parameter- ization with Vector Autoregressive factor dynamics, from which we construct a time-inhomogeneous discrete-state Markov chain approximating the joint yield process across bond maturities. This chain forms the state space of a finite- horizon Markov Decision Process in which the investor maximizes expected terminal wealth subject to proportional rebalancing costs. The optimal portfolio policy is obtained by backward induction. We also quantify the approximation error introduced by truncating the transition kernel, and show that it leaves mean terminal wealth almost unchanged while substantially distorting drawdown and tail statistics.

Power systems with increasing variable renewable generation face greater uncertainty in scheduling and balancing. Intraday and balancing electricity markets facilitate position adjustments and real-time balancing close to delivery. As delivery approaches, continuous intraday market participants exposed to imbalance settlement adjust their positions by trading additional volumes to reduce their imbalance exposure. We conjecture that positions remaining open after intraday trading, together with demand and supply uncertainties affecting physical market participants, influence price formation in the balancing market. This cross-market interaction is, however, rarely studied. To understand this interaction, this paper uses probabilistic modeling to examine how intraday orderbook information reflects subsequent imbalance price formation in Germany and Austria. We compare orderbook representations based on open, high, low, close, and volume, Volume-Weighted Average Price (VWAP), and last mid price across multiple horizons. Each representation is evaluated using the self product, neighboring products, and the product from the neighboring country. We then compare the best orderbook setting with fundamental feature sets and their combinations, followed by an ablation study of the available training history. We show that VWAP with neighboring products provides the best performance in both countries. Combining orderbook and fundamental information reduces testing loss in Germany but increases it in Austria. Using all available observations provides the best overall performance, while excluding 2022 can reduce loss for extreme price samples. These results reveal and help explain country-dependent interactions between the intraday and balancing markets.

We model market impact as the response to submitted order flow net of counterflow from latent traders, activated when price displacements from the level that would prevail without the order exceed individual thresholds. Order flow depletes this pool, and a generalized Langevin equation governs its recovery over several time scales. Its memory kernels are finite sums of exponentials, so its Markovian lift is exact rather than an approximation. For an undepleted pool, aggregation under explicit assumptions on individual trading responses yields an intermediate square-root regime between linear small- and large-order limits, without imposing a square-root impact law. Scaling thresholds and responses with price noise makes impact in this regime proportional to volatility, and thresholds that grow with the execution horizon make it independent of duration. With constant displayed depth, expected round-trip costs are nonnegative under the log-price convention, independently of the memory. Numerical experiments show that depletion narrows the square-root range and that memory spectra producing similar single-order impacts can respond differently after substantial prior trading. Calibration to market data is left to a companion paper.

Firms follow changing economic opportunities, but rivalry changes their response. We develop ESCAPE, a rational-share game of distribution-valued positioning with heterogeneous capability costs, establish a unique equilibrium, and derive an exact reallocation restriction separating opportunity and crowding contributions. Competition need not push firms apart: rational firms can enter increasingly crowded regions, because the full reallocation gain can be positive even when its crowding component is negative. Rivalry instead changes how differently firms respond to the same opportunity shift. In the benchmark many-firm economy, the relative-response component accounts for 90.5% of the weighted squared composition-response contrast between strategic and independent firms; it is numerically zero under identical capabilities. The contrast remains distinguishable under corpus-scale measurement. Corporate news distributions document persistent but changing peer structure: optimized peer reconstructions retain 86.5% of their aggregate validation advantage one year later even as absolute distance to both frozen reconstructions increases. Peer structure is persistent without being a fixed destination, so current similarity can remain informative without fixing firms' future relative positions.

We develop a non-perturbative framework for stochastic-volatility option pricing built on the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables is approximated by a self-consistent Gaussian whose mean and effective diffusion follow from the 2PI stationarity conditions, with the exponential and CEV vertices evaluated through the exact Gaussian moment-generating function rather than a Taylor cut. For exponential vertices the skeletons beyond this level sum in closed form: in exp-OU the evaluated melon level cuts the Hartree error by 20-130x, to 0.01-0.11 bp. Whether the dressed inverse propagator is local in time separates Markovian models, where the gap equation collapses to a few ODEs, from rough (Volterra) models, where the full two-time propagator is retained. At nonzero correlation the field is integrated deterministically by conditioning on its two leading Gaussian modes, with exact conditional moments and a moment-matched law for the integrated variance and leverage integral; in the CEV models the correlated drift enters a Dyson equation around the exact absorbed-CEV propagator, resummed by jumps along the variance clock. These closures match Monte Carlo references for rough Bergomi approximately at their resolution (0.01-0.1 bp) down to H=0.07, rho=-0.9, and price SABR to 0.97 bp over a 72-cell grid with maturities to ten years (75 bp for Hagan's expansion) and rough SABR to 0.92 bp. Conditional on the volatility field, forward-start smiles and continuously-monitored barriers reduce to field-only quadratures on the native Volterra field, and the causal response block yields the impulse-vega curve in one adjoint contraction. Derivations, extended benchmarks and secondary applications are in an ancillary technical supplement.

Schmelzer and Hastie prove that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. This companion note checks that result numerically with a stock LASSO solver, lars\_path from scikit-learn, and no portfolio software. It covers long–short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Every corner the path returns meets its own optimality conditions to about $10^{-13}$ and agrees with independent quadratic-programming solvers, on factor models of up to 500 assets, on the Fama–French size and book-to-market portfolios, and on daily returns of 494 S&P~500 stocks. Called naively, the long-only path stops at the maximum-Sharpe portfolio. One shift of the response, by an amount computed in advance, lets a single call reach the minimum-variance portfolio. The script, its checks, the Fama–French returns and an R cross-check are published, with a locked environment, so that anyone can repeat them.

We study the joint dynamics of the best bid and ask prices with a spread-gated Hawkes-flocking model. The model tracks four types of best-quote movements: spread-narrowing movements are switched off when the spread is at its one-tick minimum, and a cross-side excitation term, whose activation depends on the prevailing spread, links the two sides of the book. We show that the process is non-explosive on every finite horizon, give an $O(N)$ recursive likelihood, and validate the maximum likelihood estimator by simulation. On real intraday limit order book data for two large-tick stocks, INTC and MSFT, the restriction that removes the cross-side term is rejected, and the full model improves fit substantially by AIC and BIC; the likelihood is multimodal on a single day, so estimation uses a multi-start search. As an application, we derive the closed-form optimal size of a single-period limit order placed at the best or second-best quote, given the model's next-event probabilities and externally supplied execution probabilities.

In quantitative finance, standard regression losses are misaligned with the economics of return prediction. As the conditional mean of financial log-returns is close to zero, symmetric losses such as the mean squared and mean absolute errors make the constant zero forecast a near-optimal solution, penalizing models with genuine but noisy directional skill. This applies both during training, where predictions shrink toward zero, and during evaluation, where trivial forecasters can lead loss-based rankings. Under a Gaussian linear prediction model, we show that all symmetric monotonic losses share a universal breakeven directional accuracy against the zero predictor, which rises sharply and becomes unobtainable as the prediction noise approaches the standard deviation of the returns. We introduce the CZAR (Composite Zero-Agnostic Return) loss function, a piecewise quadratic loss built around five key requirements: convexity in the prediction, asymmetry with true return direction that vanishes at zero, near-linear penalization of undershoots and wrong-direction predictions, divergence for large errors, and an adaptive loss floor for evaluation. CZAR is provably convex in the prediction at fixed true value, has closed-form gradient and Hessian suitable for custom objectives in gradient-boosted libraries, and its four hyperparameters reduce to a single choice through correlated defaults. In idealized tests, the minimum directional accuracy required for a CZAR-evaluated forecaster to outperform the zero predictor under mean log loss remains near the 50% chance level, whereas the corresponding threshold for symmetric losses rises sharply with prediction noise. This advantage persists under heavy-tailed return distributions. In a LightGBM experiment on intraday BTC log-returns, CZAR-trained models reduce the `zero-returns bias' and improve directional accuracy on large-magnitude returns.

Evaluating finance research agents requires rubrics that reflect expert standards and fix the values correct as of an information cutoff. Expert-reviewed finance benchmarks rely on fixed, per-item rubrics, which are costly to extend and cannot encode each institution's own standard. In FinAutoRubric, experts specify reusable evaluation guidance, while agents and code carry out query-specific rubric generation, review, and validation. This expert guidance governs every agent, as prompts and as rules that code enforces, and a Task Bank of reusable criteria carries it across tasks. In long-horizon loops that follow the expert guidance, a writer agent researches every expected value and a reviewer agent verifies it, and failures escalate to a human. On three expert-authored finance benchmarks, its rubrics track expert scoring as closely as the strongest evaluated generator while stating the expert rubric's expected value for more criteria, their scores agree with human grading, and in-house analysts prefer them in a blind review. The released 100-query FinAutoRubric Benchmark, built from in-house analysts' key questions across 78 tasks and eight asset classes, shows that rubrics from an earlier model generation still leave headroom for a later one.