Papers

Kalshi's multivariate-event architecture produces market objects on demand from exact selected legs. Across a registered seven-day interval, 190 independently validated temporal shards yield 7,611,594 unique REST MVE market tickers after excluding 5,777 boundary-overlap observations; the population was created at an average rate of 1.087 million objects per day, with strong hourly burstiness. The hierarchy is sharply compressed relative to the market-object count: 5,262,526 exact event keys, three collection keys, 83,701 selected-leg primitives, and 66,344,938 selected-leg occurrences. The largest collection accounts for 7,217,085 objects (94.82 percent), with an effective collection count of 1.11; the effective primitive count is approximately 720. REST and WebSocket are distinct observation surfaces: 1,487,330 created-notification tickers intersect the REST population in only 276,177 exact tickers. All three observed collection keys have current endpoint confirmation without establishing historical collection or rule versions. The exact structural signature yields 7,611,594 unique signatures with zero collision groups. At retrieval, 2,692,787 objects (35.38 percent) have positive cumulative volume or open interest; all observed 24-hour-volume values are zero and trade-count fields are unavailable. This is current-snapshot activity eligibility, not historical trading. The central result is that a very large on-demand market-object population is generated by a concentrated collection layer and reused primitive vocabulary; economic breadth must be measured at several hierarchical levels rather than by ticker count alone. Exact public endpoint evidence is available for 7,357,576 MVE objects, whereas only 126,806 have an exact determination-to-endpoint pair: terminal-state coverage and lifecycle-path coverage are distinct statistical objects.

We study libraries of cross-sectional signals: at each date, a forecast vector over $d$ assets intended to predict the next period's cross-sectional return. Demeaned and unit-normalized, a signal is a point on a sphere and its $T$-date history a point on a product of $T$ spheres. A pairwise correlation cap on histories is a minimum angular separation on that product, so growing a library under such a cap is a packing problem. If a large library is not too pairwise correlated and is equally weighted, does the equally weighted sum (EWS) tend to a known principal-component quantity as it grows? We answer this under explicit assumptions on how the library is filled. Separation alone guarantees nothing: it fixes no limiting distribution; a saturated library covers the sphere yet can carry a biased count; and near-maximum packing on a fixed domain forces uniform volume, which on the unrestricted sphere gives zero mean and no distinguished principal component (PC1). Alignment depends on the admission rule and candidate distribution. Under the uniform product-volume benchmark, screening on positive average information coefficient (IC) yields a nonzero, target-aligned mean but an isotropic second moment, whereas a positive IC margin $\beta$ makat every finite $T$, with athree-level spectrum whose leading eigenvalue tends to $\beta^2$ while residual levels decay as $1/T$; margins of order $T^{-1/2}$ keep a positive admission rate but a vanishing eigengA finite residual-spectrum criteS-PC1 alignment.Gilbert-Varshamov codes show separation permits both outcomes: exponentially large positive-IC libraries exist whose EWS is PC1, and others whose EWS is orthogonal to PC1. $\log J=o(T)$ suffices for uniform estimation among $J$ candidates from $T$ iid dates. Derived results are proved and checked numerically; no market data are used.

We study coordination games in which every action requires planning and preparation. Before players act, they can revise their plans based on partially revealing information about their adversary's preparations. Precise information enables agents to screen for cooperation, selecting the payoff-dominant equilibrium either via small exogenous trembles or via payoff uncertainty. Across scenarios, we emphasize that decomposing an action into (i) preparation and (ii) execution allows us to analyze simultaneous-move games where players partially observe each other's contemporaneous actions.

As artificial intelligence's capabilities improve, it is increasingly viewed as a general scientific method. But how true are these claims? Does AI outperform all techniques, or only some, and how is this changing? To assess the claims, we assemble a corpus of 2,507 head-to-head comparisons between AI and other scientific analysis techniques across 27 scientific disciplines from papers published between 2000 and early 2025. We find a profound dichotomy. Relative to traditional statistics, AI often outperforms, but at a significantly higher computational cost. But there are also nearly a quarter of cases where AI is both more expensive and performs worse than traditional statistical techniques and this fraction has been stable for a decade. Relative to scientific computing, AI often underperforms, but at lower computational cost. This has begun to change: since 2020, AI's performance against scientific computing has notably strengthened and it now outperforms on more than half of comparisons. These patterns suggest that AI is therefore not a universal replacement for existing methods, but rather a valuable – and improving – part of a new AI-enabled scientific frontier.

Numbers this large invite a defensive reflex: reach for the reassuring figure and move on. By the most widely cited measure, the World Bank's extreme-poverty line of \$3.00 per day (2021 PPP), approximately 847 million people, or 10.4% of the world's population, lived in poverty in 2024. That figure is accurate as measured. It is also, by design, a floor: a threshold built to mark bare survival in the poorest economies, not to describe what it takes for a family anywhere to live with basic security. The central argument of this report is that the reassurance offered by that single line is largely an artifact of how we chose to measure. Held to the \$3.00 floor, roughly 847 million people are poor; held to the standards of their own societies, the number is several times larger, and even the most cautious, honest count exceeds a billion. Measured against income standards appropriate to each country's level of development, some 3.7 billion people fall below the World Bank's \$8.30/day upper-middle-income reference line, roughly 1.1 billion are multidimensionally poor, and around 2.3 billion are food insecure. These are not competing errors but answers to different questions. This report does not dispute the official data. It takes those figures as accurate and asks what they do and do not capture. It disaggregates by geography, age, and gender and supplements the monetary count with multidimensional measures of food security, working poverty, social protection, and relative poverty. It also documents a data-quality problem that runs in one direction: survey coverage is weaker in regions with the worst poverty, so official figures are far likelier to understate deprivation than to overstate it.

We study strategic trading around index reconstitution in a continuous-time, multiasset game with transient cross-asset price impact and heterogeneous beliefs about future index membership. Opportunistic traders position before a public announcement, adjust to the revealed composition, and trade around an indexer following a prescribed execution schedule. Under a no-price-manipulation condition, we construct a subgame-perfect Nash equilibrium on every finite horizon. The affine feedback policies are computed from a non-standard matrix Riccati equation and linear ordinary differential equations whose number and dimensions do not grow with the number of traders. Aggregate inventories and price impact depend on beliefs only through the population-average belief, while differences in beliefs affect individual inventory positions. Under mean-field scaling, we construct a mean-field equilibrium and obtain quantitative convergence and approximate-Nash bounds. Numerical illustrations show how competition and impact decay determine the balance between adverse price displacement from anticipatory trading and savings in the indexer's execution costs when opportunists trade against its orders during implementation.

We model the economics of recursive self-improvement (RSI) and assess its plausibility and impacts. First, we build a sequence of increasingly rich models of AI progress to highlight the feedback loops behind RSI. We represent our models as directed graphs and show that net acceleration in AI capabilities depends on the product of elasticities across each feedback loop. Second, we distinguish between "narrow" and "broad" AI capabilities, capturing the possibility that AI systems improve narrowly at optimizing AI R&D benchmarks without improving at broader economically valuable tasks. Third, we document existing estimates of key parameters and provide a wish list of empirical objects that AI companies can measure and feasibly share publicly. Finally, we calibrate the model with existing data. A back-of-the-envelope calculation suggests that feedback loops are not currently strong enough to generate a self-sustaining acceleration, though they appear to be strengthening. We conclude by assessing the plausibility and implications of such an acceleration.

We provide an introduction to real-world asset (RWA) tokenization, and develop two economic models connecting this emerging market to classical financial theory. In search for a theory of RWA tokenization, we classify RWA tokenization according to the role of the underlying asset, distinguishing standard RWA tokenization, stablecoins, and Digital Asset Treasuries (DATs). Our first model connects tokenization with security design under asymmetric information. Continuous secondary-market trading generates information recovery, reducing adverse-selection costs over time and affecting both the issuance price and the optimal tokenization design. Our second model develops a dynamic corporate-finance framework for DATs, in which market valuation, capital-market financing, and crypto accumulation interact endogenously. We characterize the optimal issuance policy and illustrate the model using Strategy as a case study. A few directions for future research are discussed, providing a starting point for further theoretical and empirical study of RWA markets.

This paper studies the strategic market participation of a monopolistic energy storage aggregator (ESA) in a day-ahead electricity market. The ESA coordinates geographically distributed storage units, submits a coordinated bid for its portfolio, and may hold financial transmission rights (FTRs). The system operator clears the market through a network-constrained, multi-period economic dispatch, determining generation and load schedules, nodal prices, energy-market payments, and FTR payoffs. We formulate the ESA–system-operator interaction as a Stackelberg game and characterize its equilibrium through a constraint-binding-pattern decomposition of the market-clearing problem. Beyond enabling equilibrium computation, the framework reveals how the ESA can increase its profit by strategically inducing or avoiding particular constraint-binding patterns. It also establishes a novel welfare result: although strategic storage without FTRs is known to weakly improve social welfare relative to the no-storage case, certain FTR positions can overturn this guarantee by strengthening the ESA's incentive to induce particular patterns, causing social welfare to fall below the no-storage level. Motivated by these findings, we develop two system-operator mechanisms for limiting undesirable ESA behavior and its adverse effects on market outcomes and social welfare. Finally, a three-bus study illustrates the theoretical findings, while IEEE test systems demonstrate the scalability of the proposed method.

Advancements in data fusion and real-time analytics technologies have opened new avenues for addressing complex domain challenges. Financial risk early warning systems often suffer from inefficiency due to information silos and monitoring delays. This paper proposes a credit risk early warning system based on heterogeneous information fusion. The system employs a model architecture integrating deep neural networks and attention mechanisms to extract multidimensional features from diverse data sources such as transaction behaviors and social networks, thereby establishing an early identification mechanism for corporate and individual credit risks. System testing demonstrates that this approach significantly enhances the accuracy and timeliness of risk warnings, outperforming traditional rule-based engine solutions. The findings offer innovative insights for early intervention in financial risks, holding practical significance for safeguarding financial stability.

The 2027 Solvency II reform recalibrates the Risk Margin by reducing the prescribed cost-of-capital rate from 6% to 4.75% and introducing a time-dependent attenuation of future Solvency Capital Requirements. This paper develops an analytical and numerical framework for characterizing the effect of the final regulatory calibration. By normalizing discounted projected capital requirements into a probability distribution over run-off time, we obtain an exact representation of the ratio between the revised and previous Risk Margins. The framework yields sharp universal and horizon-specific bounds, characterizes the effect of later capital timing through stochastic dominance, and shows that mean run-off time alone does not determine the reform effect when temporal dispersion varies. Additional bounds are derived conditional on mean run-off time and horizon. Conditional on a given projected SCR path, the mechanical reduction lies between 20.83% and 60.42%. For proportional Best Estimate projections, an exact covariance decomposition identifies how departures from proportionality affect the relative reform ratio. Holding the projected SCR path fixed, the revised formula has a lower direct interest-rate semi-elasticity than the previous calibration. A reduced-form stochastic extension further quantifies convexity effects arising from uncertainty in capital persistence. Numerical applications reconstruct Risk Margin calculations from published actuarial run-off profiles and complement them with controlled long-horizon, interest-rate, and persistence experiments. The results show that the reform effect is governed by the temporal structure of future capital and provide tractable tools for assessing projected capital profiles, Risk Margin simplifications, and direct discount-rate sensitivity.

Understanding how global supply chains endogenously transform in response to disruptions requires a parametric model of processing networks with non-neutral substitution elasticities. While cascaded CES production functions provide a rigorous analytical framework, dynamically calibrating their structural parameters from time-series data constitutes a highly non-convex inverse optimization problem. Since enforcing strict microeconomic concavity renders standard monolithic algorithmic approaches computationally intractable, we propose a novel data-driven, structure-exploiting algorithm to bypass this limitation. By leveraging the physical upstreamness topology of the supply chain, our hybrid heuristic effectively breaks the curse of dimensionality inherent in economywide processing networks. Applying this computational framework to United States time-series data, we successfully calibrate the fundamental heterogeneous elasticities. This provides a scalable analytics engine to fully endogenize complex supply chain transformations, thereby offering a practical tool to measure structural productivity and uncover the elastic origins of systemic tail risks in large-scale production networks.

An Oracle result is not yet a protocol payout, a redeemable position is not yet collateral in a holder's account, and a redemption event is not a complete measure of economic entitlement. This companion paper develops an event-sourced framework for Polymarket conditions from preparation through protocol finality and observed holder realization. The empirical design uses three Conditional Tokens Framework event families derived from a pinned contract application binary interface (ABI): ConditionPreparation, ConditionResolution, and PayoutRedemption. It separates the contract-wide acquisition universe from the frozen Polymarket adapter-question cohort. The exact bridge contains 108,638 linked conditions. Of these, 99,283 have an observed protocol-resolution event by the fixed snapshot at Polygon block 90,114,204 (2026-07-12T17:11:41Z). Among resolved exact-linked conditions, 92,158 have an observed redemption of any amount and 91,817 have an observed positive-payout redemption; condition-specific Kaplan-Meier medians from first protocol resolution are 182 and 200 seconds respectively. The exact-linked payout taxonomy contains 53,847 canonical (0,1) vectors, 45,024 canonical (1,0) vectors, 410 fifty-fifty vectors, two other valid vectors, and 9,355 conditions with no observed resolution. Cross-contract Oracle-adapter-protocol ordering is reported conservatively: 823 conditions have an interval-qualified terminal generation, 48 have multiple candidate generations, 91,638 have no compatible terminal generation in the frozen evidence, and 16,129 are right-censored or otherwise unevaluable. The formal results show that Oracle finality does not identify protocol finality, protocol finality does not identify holder realization, and redemption events alone do not identify the fraction of entitlement redeemed without an independent balance-consistent entitlement denominator.

Prediction-market resolution is often reduced to a terminal outcome and one timestamp. That representation is inadequate for leveraged event claims because rule versioning, request creation, proposal, dispute, reset, Oracle finality, and adapter terminality are distinct states with different observation precision and balance-sheet consequences. We reconstruct those states for Polymarket using Oracle request generations as the unit of adjudication. The population is frozen at Polygon block 79,721,080 and contains 185,550 initialized adapter-question instances and 350,703 decoded adapter logs. Exact requester-filtered extraction yields 504,332 decoded Oracle lifecycle events: 184,148 request creations, 159,447 proposals, 1,604 disputes, and 159,133 settlements. The accounting closes as 182,671 questions with at least one request plus 1,477 successor generations. Immutable chain identity and deployed request semantics provide exact linkage; unfinished histories remain right-censored. Request age is not semantic resolution age. Median request-to-first-proposal time is 182 seconds on the legacy route but 176,388-744,151 seconds on modern routes; post-reset successor proposals arrive within 300-2,909 seconds at the median. This descriptive contrast does not establish causal efficiency. Exact stable-ID metadata linkage recovers 104,032 of 185,550 questions (56.07%), leaves 81,518 unmatched, and produces no ambiguous exact match. External-source publication and contractual-decidability clocks remain unmeasured population-wide and are not replaced by mechanism timestamps. The results establish an event-sourced account of Oracle adjudication, semantic governance, and adapter terminality. Companion Part II reconstructs Conditional Tokens payout recording and observed redemption, preserving the boundary between adjudication, protocol settlement, and holder realization.

Frontier models score well on shallow document/chart reading tasks. In a controlled data-room audit, moving evidence into buried conditions reduced accuracy, increased forced declarations, increased tool calls, and increased cost per correct answer. Confidence and benchmark calibration did not fully capture wrong answers; a documented production incident shows fabricated structural claims can be mixed with accurate numeric tables. Agentic evaluations need claim-level receipts (statement-level provenance, not answer-level scores), condition-aware scoring, and human-adversarial verification - an auditing discipline, not a leaderboard. The setting we measure is financial due diligence; the setting we are building toward next is defense staff work, where the same buried-evidence shape appears. In both, the model is not a party to the consequences; the person who signs is. In plain terms: in the documented cases we examine, agents can pair accurate numbers with confident fabricated explanations, and the burden of proof must therefore move from the model to the evidence trail.

Return models for risk-neutral financial valuation based on skew Brownian motions (SBMs) have been introduced about twenty years ago, and have recently enjoying growing popularity. Unfortunately, the story behind their development is one of mistakes and erroneous interpretations, beginning from the foundational misrepresentations that the prevalent financial model is based on the Itô-McKean SBM – which, in fact, it is not. Besides, and more seriously, the clarification of \cite{rossello2012arbitrage} that price models with a local time in their returns, such as the SBM, are arbitrageable has been, by and large, ignored. In this paper, we try to clear the field from the confusions and misconceptions lurking in the standing option pricing literature on SBM, by exposing all the errors we could trace in the treatment so far. Recognizing however the potential of the SBM skew-normal marginals for risk-neutral valuation, as a positive contribution, we reformulate the putative SBM call pricing formula and show that, even if the SBM return model admits arbitrage, its option pricing formula does not. The correct Markovian SDE with skew-normal marginals is then identified, its strong well-posedness shown, and by exploiting the availability of closed formulae, an asymptotic analysis of the implied volatility surface is offered. En route to our conclusions, we obtain a novel normal/skew-normal stochastic dominance property of independent interest.

Retail proprietary-trading firms sell a two-stage product: a paid evaluation that must reach a profit target before breaching a trailing drawdown, then a funded account that must survive a minimum window and a consistency rule before a payout. We show the geometry of this contract creates incentives that differ by stage and make passing a poor standalone signal of skill. Under end-of-day trailing the evaluation rewards a fast, lumpy cadence while the funded account punishes it, by a factor of nine in the joint gate. The evaluation is defeatable at zero skill: position sizing alone yields a pass probability near 0.40, against a measured cohort rate of 0.168. Pass probability rises with skill, but a real edge and aggressive sizing move it by nearly the same amount, so a pass rate confounds the two. Under a simplified contract model the seller's margin is bounded by the gap between perceived and actual gate probabilities, the probability analogue of shrouding a price component; the observed design, a permeable marketed evaluation and a hard payout gate, is consistent with that. Across the sector, pass rates are published far more often than payout rates. The same geometry produces negative expected value: within the measured strategy universe, no configuration at observed drifts clears break-even on any account sourced. Break-even lies between a 40.5% and 41.5% win rate at 1:1.5 net of costs, against a driftless 40.0%. The delta-neutral construction firms prohibit is approximately expected-value neutral at the observed payout ceiling. Every account-level result is reported against a zero-edge control.

Does authority in AI teams improve the outcome? Organizational theory asserts that authority facilitates decision making, improving quality. Meanwhile, some nascent AI research suggests that revision under authority makes LLM output worse. Multi-agent LLM frameworks default to giving a Manager agent the authority to send a worker's output back for revision. Prior comparisons test the effect of authority using verifiable tasks. We conduct an experiment on an open-ended task, business-intelligence reporting, using a sample of 43 paired laptop products and 86 runs. Each report is written once by a hierarchical team and once by a flat team. We find that flat teams produce higher-quality reports, scoring higher on Utility (d = 0.42, p = 0.009) and Writing Clarity (d = 0.34, p = 0.030). The reports are the same length, but hierarchical team reports use 53% more hedging words such as "may" and "could", and each revision is associated with a 0.14-point drop in Writing Clarity on a 1 to 5 scale. Before any revision, the hierarchical team's first draft is indistinguishable from the flat team's report. In other words, the quality gap can be traced to revision. Authority improves quality when the Manager can verify the work, else when it can only provide feedback it has a negative effect on quality.

After the arrival of transformative artificial intelligence (TAI), broad-based automation is expected to decrease the labor share and increase income and wealth inequality. Although economic growth is likely to accelerate, most of its gains may accrue to a narrow group of individuals and firms. Hence, if unmitigated by redistributive policy, income and wealth inequality may rise to levels unseen in the industrial economy. Using a unifying theoretical framework, we survey the redistributive policies proposed for the era of TAI, such as universal basic income (UBI), universal basic capital (UBC), state-issued compute and robot permits, and taxes on capital, compute, robots, tokens, land, energy, consumption, and wealth. We argue that policies that are able to broadly distribute rents from capital including compute and robots - such as UBC or UBI financed through capital taxes - are most likely to achieve lasting reductions in inequality in a world with human-aligned transformative AI.

Hybrid Deep Learning for equity index forecasting is limited by three problems: propagation of OHLCV noise into derived technical indicators (TIs), channel-indiscriminate multi-scale decomposition that conflates heterogeneous frequency signatures, and static multi-branch fusion that cannot adapt to market regime shifts. WaVeFuse addresses these limitations through a unified dual-branch architecture. Symlet-4 wavelet denoising (level 2, MAD soft threshold) suppresses microstructure noise in OHLCV. Seven low-lag TIs computed from denoised prices are encoded by a causal channel-wise continuous wavelet transform (Morlet, 32 scales) into a per-timestep scale-space matrix. A CNN-BiLSTM branch captures temporal dynamics, while a dual-layer Transformer (heads=4, dk in {16, 32}) models inter-scale spectral dependencies, and their representations are integrated by a 2-token softmax gate Vertical Attention Fusion (VAF) that dynamically reweights branches as market regimes shift. Evaluated under walk-forward validation (WFV) on KOSPI, DAX, NYSE Composite, and Russell 2000 (2010-2023), WaVeFuse achieves R2 = 0.81-0.96 and directional accuracy 70.5-78.3%. It outperforms seven state-of-the-art models by 8.9-20.2% MAE across twelve dataset-period configurations. Diebold-Mariano statistics (4.62-10.38, p<0.001) confirm superiority over a well-tuned XGBoost benchmark across four indices. Ablation verifies component-wise contributions. Under realistic backtesting with 10 basis point transaction costs, WaVeFuse's directional strategy achieves a mean Sharpe ratio of 3.69 across four markets and limits maximum drawdown to 7.5% during the COVID-19 crash. With 152k parameters (0.68MB) and sub-1.3ms GPU inference, WaVeFuse delivers a computationally efficient, regime-robust framework suitable for research and decision-support deployment.

Claim narratives, images and sensor data contain information about insured risks that is difficult to use through existing actuarial models. Foundation models learn patterns from large datasets before being adapted to particular tasks. By turning these high-dimensional sources into variables or numerical representations, they could help insurers use more of the information they already collect, potentially reducing the experience needed to develop each application. For example, a language model could identify a worsening injury in a new claim note, allowing a reserving model to recognise the change in expected cost before the payments reveal the deterioration. In this paper, we review language, vision, geospatial, time series, tabular and scientific models, explaining existing insurance applications and potential future uses. Scientific models extend this approach to future weather and climate conditions: their simulations can inform loss estimates once local hazards are linked to asset damage, repair costs and insurance coverage. We propose a process to connect these model outputs to actuarial calculations and to assess their predictive contribution, stability and compliance with rules on information use. Evaluating these applications is difficult when final claim costs become known only after long delays, large losses are rare or patterns learned elsewhere fail to transfer to the target portfolio. Richer data can reveal private information and support finer risk classification, which can change access to insurance. Reusing the same models across insurers also creates dependence on shared predictions and providers.

This paper studies how Chile's three largest pharmacy chains moved from the price war to collusion, using court-record daily prices and a structural model. After a court-ordered advertisement ban ended the comparison campaign, the estimated gain from loss-leader pricing fell sharply, weakening the incentive to continue the price war. The chains then used an upstream supplier as intermediary to verify a collusive price-leadership procedure. Once verified, they applied it to restore margins on former loss leaders. They then raised prices further to extract rents. These increases spread more slowly than margin restoration. The Adaptive Confidence specification allows a subjective belief about follower participation to update. It more closely matches the cumulative spread of rent extraction than the Unit Confidence specification. Unit Confidence imposes the rational-belief benchmark by fixing the leader's weight at one.

Against the backdrop of digital transformation and stricter regulation, enterprise compliance work demands higher efficiency and accuracy. The auxiliary compliance process has become an important entry point for optimizing the compliance system due to its strong transactional nature and high degree of repetition. This study focuses on the process characteristics of auxiliary compliance work, sorts out its structural composition and organizational mechanism, proposes an optimization path with process reengineering, system modeling, and technology integration as the core, and focuses on exploring the collaborative application of key technologies such as RPA, rule engine, and semantic recognition in process automation. Research suggests that the systematic optimization and intelligent upgrading of auxiliary processes will help build a modern compliance operation system that is responsive, efficient, structurally clear, and risk controllable.

This paper proposes an investment strategy through resource allocation into Kalshi Crypto Event Contracts in order to effectively hedge exposure to spot asset volatility. Using Bitcoin as a proof of concept, we treat corresponding Kalshi markets on the asset's future price as option contracts, and through construction of different portfolio allocations present a framework for which event contracts can be effectively utilized by retail investors in order to control risk framework without reducing underlying exposure to spot volatility. We showcase this information through analysis of three separate Kalshi event contracts, all relating to a different underlying market regime (i.e bullish, bearish, flat), and provide a comprehensive risk profile for each regime. Results show that a dynamic Kalshi/Bitcoin hedging strategy outperforms more simplistic portfolios across all regimes, supporting our initial hypothesis. We discuss further considerations which can erode profits in the future (i.e. fees), and provide direction for future research.

Normalized implied-volatility coordinates reveal no-arbitrage structure that is less transparent in strike space. This paper centers on a single quantity that gives those coordinates a direct probabilistic interpretation.

Managing drawdown, the peak-to-trough decline in an investment portfolio's value, is a precondition for long-term survival in practical investment management. However, mainstream stock forecasting methods predominantly optimize returns or Sharpe ratios under the independent and identically distributed (i.i.d.) assumption. Real markets do not follow this assumption, triggering catastrophic drawdowns. We propose a cross-asset state-space trading system (CAST), consisting of two components: The predictor, Cross-Asset Collaborative Kalman Filter (CoKF), estimates each asset's latent state online, coupling all assets through their correlations and adaptively fusing multiple integrated-random-walk orders. The controller, Model Predictive Control (MPC), converts the predictor's forecast into trades, using forecast uncertainty as an explicit risk penalty that controls drawdown. We evaluate CAST on four real-world stock markets over a 15-year test window and show that it consistently occupies the return-drawdown Pareto frontier, achieving strong risk-adjusted performance while maintaining substantially lower maximum drawdown than competitive baselines. A stress test across crisis periods further demonstrates robust behavior under market shocks and distribution shift. Because the predictor and controller interact only through the predicted price path, both are plug-and-play, making CAST a modular, interpretable trading system. The code is available at https://github.com/FanBroWell/CAST

Special Markowitz (SM) regularises returns and covariance jointly, relative to a reference state (mu_ref, Sigma_ref). Each eigendirection of the whitened relative operator carries a signed spectral potential Phi_k, with persistence factor psi_k = exp(-Phi_k) > 0. Positive potentials attenuate empirical deviations from the reference geometry, zero potential preserves them, and negative potentials amplify them. The persistence factor psi_k governs both the return signal and the covariance deviation: the regularised deviation from the reference is psi_k times the empirical deviation. The logarithmic potential coordinate is characterised by a multiplicative composition law on the multiplicative group of positive real numbers; the Stein loss is characterised as the unique free-energy density (within a natural class) compatible with the resulting coupling. The SM pressure functional is additive across modes the defining property of Special Markowitz.

We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadratic variation of the log price given its terminal value, up to a smaller-order term, for bounded standardized log-strikes. The framework incorporates small volatility-of-volatility, fast mean-reverting, and short-maturity asymptotics.

Reinforcement learning trading systems published in the academic literature overwhelmingly rely on price-aggregate state representations (OHLCV bars) or limit-order-book depth features, leaving microstructure pattern theories from the practitioner literature, namely Auction Market Theory and Market Profile, without a peer-reviewed computational instantiation. We present ViperQ, a reinforcement learning system whose state representation is built explicitly from Auction Market Theory primitives: Volume Point of Control, Value Area position, Low Volume Node flags, Cumulative Volume Delta divergence, and tape-velocity signatures, assembled into a 20-dimensional Z-normalised vector. Two Proximal Policy Optimisation agents are trained with a prospect theory-grounded asymmetric reward function that penalises losing holds at a magnitude consistent with Kahneman and Tversky's loss-aversion coefficient. Evaluated on a held-out twelve-month partition of institutional tick data the agents have never seen, ViperQ achieves +163.6% ROI on TSLA (-27.5% max drawdown, 27,019 trades) and +116.5% ROI on NVDA (-47.8% max drawdown, 12,892 trades) under zero leverage. The results establish Auction Market Theory features as a tractable structured input modality for sequential decision-making on financial time series and motivate further work on microstructure-aware policy learning.

We consider two canonical market-microstructure regularities: the long-memory of trade signs and the square-root law of meta-order impact. The point is not to propose new empirical laws, but to separate the clocks on which existing laws are defined. The sign-memory law is an event-time statement about the ordering and fragmentation of hidden orders. The square-root impact law is an operational-time statement about front motion in a locally linear latent order book. Starting from a discrete-time random-walk bid/ask reaction–diffusion order book with a separate event clock, we identify an event-time imbalance reduction, derive the operational-time front and impact equations in the locally linear regime, and then subordinate both sign and impact observables to calendar time. Fractional or tempered clock effects enter through this event-to-calendar projection, not through a different operational-time impact mechanism. This gives a compact clock-aware framework in which event-time sign persistence, operational-time square-root impact, and anomalous calendar-time effects appear as distinct but compatible consequences of a common order-book representation.