We provide a formulation for optimal option portfolios under Sharpe Ratio maximization when the underlying returns follow a skew-elliptical t-distribution. This departs from the traditional normal returns setting in the context of Sharpe ratio maximization by allowing the modelling of heavy-tailed and skewed dynamics. The novelty of this paper and our main result is to provide explicit formulas for the portfolio weights when maximizing the Sharpe ratio and return-to-Value-at-Risk (VaR) ratio in the skew-elliptical setting. Numerical experiments reveal that the optimal portfolios for the two ratios are different.

We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidden-cell surface-completion RMSE in the 0.94-1.56 vol-point range across both markets and mask rates 10-50%. The hybrid predictor attains 0.83 vol points at 50% masking against 7.00 for the smile re-fit alone, an eightfold reduction obtained at no additional inference cost. Under structurally-correlated hole patterns that emulate the withdrawal of an entire tenor of strikes, the smile re-fit incurs 9.6-13.1 vol points of error while the learned model remains at 1.5-1.9, isolating a regime in which the generative model is the only viable predictor. Joint training on BTC and ETH improves the in-distribution model on both markets by 9-27% relative to the better-performing single-symbol counterpart, indicating a substantially shared vol-surface manifold across the two largest cryptocurrencies over the observation window. The hybrid is calendar- and butterfly-arbitrage-free at the listed strikes, a property that the parametric smile re-fit alone fails at high mask rates. The per-snapshot reconstruction error of the trained model flags the late-October ETF-anticipation rally and the August $17$, $2023$ flash crash as elevated-error periods without supervision. All training and evaluation infrastructure is released to support reproducible follow-on work.

Cryptocurrency markets are prone to violent, synchronised drawdowns, challenging the claim that a basket of crypto-assets offers genuine internal diversification. Because standard covariance-based metrics fail to capture asymptotic tail dependence, they systematically understate systemic risk and overstate diversification benefits precisely when markets crash. This study maps the conditional dependence structure of the cryptocurrency market directly in the joint tails, isolating direct extremal linkages from those mediated by the rest of the system. We analyse the daily returns of the thirteen largest cryptocurrencies over a sequence of 89 overlapping windows spanning late 2021 to 2025. We apply dynamic Hüsler-Reiss graphical models of extremes, estimated separately for joint crashes and rallies, and benchmark them against a Gaussian graphical model of ordinary co-movement. The results reveal a near-complete and stable lower-tail graph, an upper tail that thins over time to re-form sectoral structures, and the dissolution of ordinary token categories into a single block anchored by a Bitcoin-Ethereum core. These findings imply that intra-crypto diversification fails on the downside, standard risk models underestimate market-wide crash probabilities by roughly eight-fold, and dynamic extremal graphs offer a superior tool for systemic risk monitoring.

We study the dependence of the fractional Riccati equation in the rough Heston model on the Hurst parameter $H$. For each expansion point $H_0\in(-1/2,1/2]$, we derive a Taylor expansion of the Riccati solution in $H$, whose coefficients are characterized recursively as solutions of linear Volterra equations with fractional-logarithmic kernels. We prove local uniform convergence of the resulting Taylor series and, in particular, analyticity of the fractional Riccati solution in the Hurst parameter. Through the affine transform formula, this yields approximations of the rough Heston characteristic function and Fourier prices. Numerically, once a reference solution at $H_0$ is available, the expansion coefficients can be computed recursively and evaluated for many nearby values of $H$. We implement the method around $H_0=1/2$, using the classical Heston solution, and around $H_0=0$, using a Padé approximation. Experiments for European call options indicate that low expansion orders already provide accurate implied volatilities across a wide range of Hurst parameters, including the hyper-rough regime.

We study how forward hedging reshapes incentive provision inside the firm. We consider a risk-averse producer facing demand and production risk that can either operate in-house or delegate production to a risk-averse agent under moral hazard, while hedging output in a competitive forward market with a rational market maker. Within a tractable continuous-time CARA framework, we jointly characterize optimal production, compensation, and static hedging in equilibrium. Delegation and external hedging are partial substitutes because both create value through risk sharing. Delegation can increase firm value even when the agent uses the same technology and is more risk averse than the principal, while access to forward hedging reduces the need to provide incentives through risk exposure. This mechanism delivers two main results. First, the principal hedges less under delegation than under in-house production. Second, this lower hedging demand under delegation raises the equilibrium forward price relative to the integrated benchmark. In the constant-demand case, we show that access to hedging lowers the agent's expected compensation under delegation. Numerical results indicate that this mechanism remains robust in the presence of demand uncertainty. More broadly, our results show that external risk transfer through financial markets feeds back into internal organizational design.

Energy policy is often guided by a small set of least-cost pathways to net-zero emissions, despite wide uncertainty in technology performance, fuel prices, demand and weather. To avoid overstating confidence in any single pathway, we quantify the likelihood of alternative technology pathways and identify the assumptions driving divergence, including the conditions under which technologies reach critical tipping points in competitiveness. We couple a sector-linked national optimisation model with Monte Carlo sampling (10,000 runs) across two European power systems (Germany and Great Britain) to generate probability distributions of capacity expansion and robust cost thresholds for key technologies. Results reveal substantial ambiguity in the future roles of wind versus solar, gas with carbon capture, and negative-emissions options. Tipping points vary widely with system conditions, while cross-country differences highlight the role of institutional constraints and resource endowments. Britain exhibits an either-or decision around nuclear power, investing if costs in 2035 fall below EUR 4700/kW, otherwise favouring offshore wind. Germany's uncertainty centres on dispatchable low-carbon options: gas with carbon capture (below EUR 2100/kW), biomass with carbon capture (below EUR 4200/kW), or hydrogen if electrolysis is below EUR 560/kW. We reframe scenario analysis as risk management by linking uncertainty to cost targets and minimum deployment requirements for robust net-zero strategies.

Paper A defines a time-consistent actuarial runtime that prices each side-effect-bearing action against a contractually fixed safe default and gates execution against a reserve budget. It treats the operator as passive. This paper makes the operator strategic. We characterise a five-attack space for autonomous AI-agent insurance contracts and prove when the actuarial runtime is gaming-resistant. Two attack surfaces -- post-toll safe-default selection and within-boundary action splitting -- are closed by Paper A's minimal-authority and no-splitting clauses. The remaining three require new contract clauses. First, common-control aggregation prevents cross-boundary re-routing from reducing toll below the boundary potential applied to total exposure. Second, interface failures such as invalid JSON are contract-relevant events, not safety wins: treating them as zero-toll safe defaults can reward unreliable models, while escalation fees reverse the incentive. We validate this interface-compliance theorem on committed cross-model traces from the companion empirical paper. Third, a model-identity menu with a componentwise-minimum penalty schedule makes truthful reporting of the deployed model weakly dominant. We then compose these clauses with Paper A's runtime guarantees to obtain joint incentive compatibility over the five-attack space. Finally, a two-parameter premium family discharges operator individual rationality and weak budget balance at the truthful equilibrium. The result is an incentive-compatibility layer for actuarial control of autonomous-agent side effects.

Starting with a coupled discrete reaction--diffusion formulation for the lit and latent order books with non-uniformly sampled event times and meta-order source terms we show how two familiar market-microstructure regularities can emerge from this framework: the long-memory of trade signs associated with the Lillo--Mike--Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact. This uses the well known locally linear order book and constant participation-rate execution in the front dynamics to reduce the dynamics to a Volterra equation whose leading-order solution then yields the well know result of concave impact trajectory, and a completion impact proportional to the square root of the meta-order size. We then re-derive the heavy-tailed Pareto-distributed meta-order lengths induce a power-law trade-sign autocorrelation through the interface source term to discuss the interface representation. These are familiar derivations, what is slightly different here is that we reinterpret these known derivations to make it clear that LMF law is an event-time sign-memory statement, whereas the square-root law is a physical-time viability statement where non-uniform event waiting times can alter the calendar-time impact trajectories depending on the mappings and interpolation used to set continuum operational time.

Over the past decade, U.S. policies have increasingly aimed to preserve artificial intelligence (AI) leadership by promoting domestic free-market policies while controlling global technological chokepoints, particularly advanced semiconductors and computational infrastructure. These measures raised the cost of Chinese AI development, but they also increased the strategic value of open and locally adaptable AI systems. Before raising export controls on high-performance chips, both the U.S. and China promoted policies that included support for open-source AI. During the period following major U.S. export-control shocks, China increasingly embedded open-source AI into national technology strategy through proposed ecosystem building, standards coordination, and resilience-oriented deployment. Moreover, Chinese developers increased engagement with open-source large language model repositories substantially more than U.S. developers did, consistent with a shift toward open infrastructure under geopolitical constraints. Subsequently, Chinese-origin open models diffused widely through open-source communities and scientific research. Even though such models remained largely absent from U.S. patent disclosures, American commercial entities use them in open-access research, suggesting their undermeasured importance within the foundation of U.S. commercial activity. These findings suggest that technological containment policies may unintentionally accelerate open innovation ecosystems as a competitive response, with implications for global leadership in both academic and commercial artificial intelligence.

Production is a sequence of steps that can be executed (1) manually, (2) augmented with AI, or (3) fully automated within contiguous AI-executed steps called ''chains.'' Firms optimally bundle steps into tasks and then jobs, trading off specialization gains against coordination costs. We characterize the optimal assignment of humans and AI to steps and the firm's resulting job structure, showing that comparative advantage logic can fail with AI chaining. The model implies non-linear productivity gains from AI quality improvements and admits a CES representation at the macro level. Empirical evidence supports the model's key predictions that (1) AI-executed steps co-occur in chains, (2) dispersion of AI-exposed steps lowers AI execution at the job level, and (3) adjacency to AI-executed steps increases the likelihood that a step is AI-executed.

A game of information concerns two players transmitting messages that are obscured by noise. A receiver digests the combination of the two information sources and makes an assessment rationally. The aim of the players is to generate opposing assessments for the receiver by choosing signal-to-noise ratios of their information. It is shown that this problem can be reduced into an elementary infinite game on the square, thus admitting a complete equilibrium solution. Three generalisations of the game are proposed.

First, we present a new theory of "modular natives." A modular native is a basic building block that is born modular, e.g., a solar cell. The theory predicts that using modular natives in building things reduces complexity and improves predictability, resulting in better outcomes and faster scale-up. Second, we test the theory on the largest dataset of its kind. We find, at a high level of statistical significance, that modular natives operate under a fundamentally different risk regime than other project types, with finite and predictable risk, in contrast to non-natives that have infinite and unpredictable risk. The findings help explain why modularity is key to successful building while bespokeness often leads to failure. Third, we relate our findings to economic and geopolitical development, arguing that China understands modular natives and scale-up better than any other geography and that this is key to China's swiftly growing dominance in renewables, batteries, EVs, robots, etc. We argue that China's mastery of modularity and scale-up is a major innovation in its own right, among the greatest and most impactful in human history, falsifying the common notion that China cannot innovate. Business and government outside China ignore these findings at their peril. Finally, we spell out policy and practice implications and identify areas for further research.

We introduce the Multiplex Network Hawkes model, which extends the network Hawkes framework of Linderman & Adams (2014) by allowing multiple excitation layers whose weights depend on observed edge and node covariates. We use the model to investigate how contagion in financial networks is affected by different transmission channels. The multiplex structure separates channel-specific contributions within a single inferred transmission network, allowing candidate propagation mechanisms to be compared directly rather than being absorbed into one homogeneous excitation layer. Covariate-dependent excitation allows us to investigate sources of transmission. We make posterior inference about the inferred directed network and its excitation dynamics using an MCMC sampler. The application uses a broad cross-industry credit default swap (CDS) dataset of 99 North American and European firms, including banks, insurers and non-financial firms over 2004-2022. We evaluate three candidate contagion channels associated with asset similarity, solvency and profitability. The results indicate sparse contagion pathways, with systemic-risk transmission concentrated in outward flows from a small number of influential institutions rather than in mutual feedback between institutions. The channel results show that industry similarity is the most consistently supported asset-similarity effect, while aggregate layer contributions indicate that asset-similarity, solvency and profitability channels all contribute to inferred excitation.

Sunshine trading theory predicts that publicly disclosing trading intentions can reduce adverse selection and attract liquidity provision, lowering execution costs. Evidence is scarce, because explicit preannouncement of large orders is rare in traditional markets. We study Hyperliquid, a fully on-chain limit order book for cryptocurrency perpetual futures, where protocol-native TWAP orders disclose their terms from inception and remain visible while active, a natural form of sunshine trading. Using address-level data, we reconstruct 4.3 million hidden metaorders and compare them with 465,000 visible TWAP executions. The two execution styles differ sharply: hidden metaorders follow front-loaded, U-shaped schedules consistent with transient-impact optimal execution, whereas TWAPs trade nearly uniformly. We test the preannouncement predictions of Admati and Pfleiderer (1991). Visible TWAPs face lower execution costs than comparable hidden metaorders and leave a smaller permanent price impact. Hidden metaorders executed alongside already-visible same-direction TWAP flow incur higher permanent costs: adverse-selection costs shift toward non-announcers. Finally, visible TWAP programs elicit liquidity provision: while active, displayed depth rises and the book tilts toward the absorbing side, the more so the larger the announced order.

Transformers have shown remarkable success in sequence modeling, yet their direct application to financial time series remains challenging due to noisy signals, short-memory dynamics, and distributional shifts. This paper proposes a modified Transformer architecture for one-step stock index forecasting, combined with advanced learning-rate scheduling and a novel Shifted Data Augmentation (SDA) technique. We evaluate the proposed framework on two benchmark stock index datasets, VN30 and S&P 500. Experimental results demonstrate that cosine annealing with warmup consistently improves forecasting accuracy over the generalized inverse-power scheduler. Furthermore, SDA substantially reduces forecasting errors and run-to-run variability while improving robustness to hyperparameter selection. The combination of cosine annealing scheduling and SDA achieved the best performance on both datasets, indicating that data augmentation can play a more important role than increasing model complexity in Transformer-based financial forecasting. These findings provide a practical and computationally efficient approach for robust stock index forecasting in noisy financial environments.

Many models in quantitative finance have no closed-form option prices and rely on slow, noisy Monte Carlo simulation; neural surrogates restore speed but offer no error guarantees. We present a general recipe for surrogates that are fast, with bounded and verifiable error, applicable to any simulation-based density model. A Mixture Density Network maps parameters and maturity to the terminal return density as a Gaussian mixture, so prices, implied volatilities, and Greeks follow in closed form as an arbitrage-free mixture of lognormals, with a CDF-matching loss aligned to pricing error. A distribution-free Monte Carlo noise floor, $\sqrt{1/(6N)}$, quantifies the best accuracy achievable at a given simulation budget and decomposes the out-of-sample error into four controllable terms. We demonstrate the method on GJR--GARCH, where the surrogate reaches an out-of-sample CDF error of $1.4\times10^{-4}$, within $10\%$ of the noise floor, and prices each option in a few microseconds on a single CPU core, or under a microsecond on a GPU.

Agentic AI systems create model risk because uncertain beliefs are coupled to autonomous actions. This paper develops a mathematical framework for quantifying agentic AI risk by representing the system as a partially observed Markov decision process with latent states, Bayesian belief updates, control-dependent losses, and tail-risk functionals. The main methodological contribution is to treat a large language model as an uncertain semantic observation model: the LLM maps high-dimensional evidence into a probability vector over latent regimes, while a Bayesian filter imposes temporal coherence and produces auditable posterior beliefs. The resulting framework separates uncertainty quantification from risk measurement. Uncertainty is represented by posterior entropy, belief drift, and calibration error; risk is represented by the distribution of losses induced by decisions taken under those beliefs. The paper connects this construction to model risk management, coherent risk measures, Bayesian filtering, POMDP theory, robust control, and quantitative portfolio risk. An empirical case study using adjusted daily equity returns from Massive.com illustrates how LLM-inferred belief states can be combined with Bayesian filtering to produce regime probabilities, uncertainty diagnostics, calibration statistics, and VaR/CVaR-style risk measures. The framework is intended as a rigorous foundation for validating agentic AI in financial and other regulated decision environments.

Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.

We present a machine-checked development of the $L^2$ Itô calculus of Brownian motion on a bounded time interval $[0,T]$, formalized in Lean 4 on top of Mathlib and the BrownianMotion package. The development contains: the construction of the Itô integral as an isometry of Hilbert spaces, from a predictable-rectangle $π$-system through the density of simple adapted processes; the Itô integral as a process, proved to be an $L^2$-continuous martingale through a single structural identity (the integral at time $t$ is the conditional-expectation projection of its terminal value onto $\mathcal{F}t$), from which adaptedness, the martingale property, the contraction bound, and both the terminal and the time-indexed Itô isometries follow as corollaries; and Itô's formula for $C^3$ functions with bounded derivatives, including its time-dependent form $df = f_x,dB + (f_t + \tfrac12 f{xx}),dt$, obtained by a discrete-to-continuous argument through weighted quadratic variation and explicit $L^2$ remainder bounds. To our knowledge this includes the first machine-checked proof of Itô's formula, and the first machine-checked construction of the Itô integral as a martingale-valued process, in any proof assistant. We are deliberate about the boundary: the theory is the $L^2$ theory on $[0,T]$ with bounded-derivative integrand classes; localization to the unrestricted $C^2$ formula, integrators beyond Brownian motion, and pathwise statements are out of scope, and we say precisely why and where. The development is roughly 7,200 lines of Lean across 22 modules; every theorem is sorry-free, the axioms of each headline result are pinned to Mathlib's classical defaults by a build-enforced gate, and the whole is reproducible from a pinned toolchain.

Models whose predictions depend on only a handful of well-constrained parameter combinations, termed sloppy models, are ubiquitous in nonlinear stochastic systems. The information-geometric approach to sloppiness advocates using the symmetrized Kullback--Leibler divergence and its associated Hessian, the Fisher Information Matrix (FIM), as the natural loss function. However, prior applications have relied on analytically known or parametrically fitted distributions. In practice, for general agent-based or stochastic models the distribution must be estimated from simulation data. I demonstrate, using Kirman's ant recruitment model as a worked example, that a standard kernel density estimate (KDE) converges to the analytical FIM eigenvectors and eigenvalues with simulation budgets accessible in practice. I derive the analytical Hessian in closed form, show numerical convergence of the KDE-based estimate as a function of simulation data, and demonstrate how the stiff direction enables efficient phase exploration across the model's unimodal and bimodal regimes.

This paper develops a climate-aware pricing framework for excess-of-loss (XL) reinsurance contracts and catastrophe (CAT) bonds under non-stationary catastrophe risk. Catastrophe arrivals are modeled as a Cox process whose stochastic intensity depends exponentially on a temperature-related climate index. To represent climate dynamics, the index is modeled as a mean-reverting Ornstein--Uhlenbeck process around a time-dependent warming trend. Within this setting, aggregate losses follow a compound Cox structure with lognormal severities. Pricing is performed under a reduced-form risk-adjusted measure, which provides a tractable valuation approach for XL reinsurance layers and binary zero-coupon CAT bond payoffs in an incomplete market setting. Because catastrophe losses are not dynamically replicable, the framework emphasizes scenario-based valuation rather than model-independent no-arbitrage bounds. A Monte Carlo valuation scheme is implemented to quantify the economic implications of climate-dependent catastrophe intensity. The numerical results show that climate dependence materially changes the loss-generation mechanism and affects the valuation of catastrophe-linked contracts. In the baseline calibration, the climate-aware model increases the excess-of-loss reinsurance premium and lowers the CAT bond price relative to the stationary benchmark. Furthermore, our analysis of the 99.5\% Tail Value-at-Risk (TVaR) indicates that stationary benchmarks may underestimate economic capital requirements by approximately 13.7\% compared to the climate-aware framework, highlighting the potential regulatory relevance of the proposed model. This finding highlights that benchmark design is critical for interpreting climate-pricing effects.

Two communities that rarely cite each other -- spatial statisticians fitting high-dimensional weather fields, and quantitative investors building portfolios -- have independently arrived at the same mathematical object: a Schur complement, damped by one interpretable parameter. In spatial modeling the Schur complement is the conditional covariance that makes a Gaussian (Vecchia) pseudo-likelihood estimable at scale, and recent work regularizes it by shrinking toward a base model. In allocation it is the residual risk of a bet net of its hedge, and the same parameter interpolates hierarchical risk parity and the minimum-variance portfolio. We show these are one operation -- reliability shrinkage of a conditional Gaussian -- so that the damping a weather model needs to remain estimable when stations outnumber observations is, term for term, the damping a portfolio needs to remain stable when assets outnumber returns. The optimal amount is a closed-form reliability, a James-Stein shrinkage that is simultaneously a Ledoit-Wolf intensity. The shrinkage machinery is classical, but the identity appears to be new: to our knowledge neither literature has noted that the conditional shrinkage a spatial model fits and the diversification-variance tilt a portfolio chooses are one and the same quantity. We make the correspondence precise, note that the two literatures have each supplied what the other lacks, and report a small experiment on the one genuinely open choice -- how to set the damping -- suggesting the spatial community's fitted intensity is, if anything, the better recipe.

Helicopter emergency medical services (HEMS) provide rapid access to critical care but are costly to operate and difficult to sustain financially. A clear understanding of these costs is essential for evaluating the feasibility and design of population-based funding or policy strategies. We developed a two-part model: (1) a cost framework capturing capital and operating expenses (e.g., aircraft, equipment, labor, facilities), and (2) an actuarial revenue model using healthcare encounter data and payer reimbursement rates. The model was applied to a commercially insured Massachusetts population (3.9M lives), using provider charge data and Medicare fee schedules. We analyzed breakeven transport volumes under varying reimbursement and labor cost assumptions, including sensitivity scenarios. Under optimistic assumptions (full charge realization, minimal overhead), breakeven is reached with approximately 90 annual transports. More realistic scenarios, incorporating commercial reimbursement at 50% of charges and full 24/7 staffing, require 184 transports. If labor costs are doubled or Medicare rates are used exclusively, breakeven thresholds exceed 1,000 transports per year. A Monte Carlo simulation (10,000 iterations) confirmed the robustness of these thresholds: the median simulated breakeven was 190 transports under commercial reimbursement, closely matching the deterministic base case. The 90th percentile reached 304 (commercial) and 1,066 (Medicare) annual transports. HEMS programs are highly sensitive to labor costs and payer reimbursement levels. Sustainable operation requires more transport volume than previously estimated, especially when reimbursement is constrained or staffing costs increase. This model provides a transparent, replicable tool to inform financial planning, policy evaluation, and payer negotiations for air medical services.

Given risk-neutral densities of a tradeable forward, fitted as $N$-component mixtures at a finite set of expiration pillars, we look for a continuous-time interpolation that is (i) \emph{mixture-preserving}, remaining a mixture of the same kernel (generically with more components than either pillar), and (ii) \emph{arbitrage-free} across expiries. The second requirement is the \emph{peacock} (convex-order) property, equivalently a non-negative Dupire local volatility; for full-support kernels (Gaussian, lognormal) it gives a unique continuous local-volatility diffusion (Lowther). We construct such an interpolation in a fixed $2N$-component family, freezing both pillars' components and moving only their weights. Applied to mixture term-structure models, it lifts Brigo--Mercurio to time-varying weights and reaches the free-per-strike-width generality of SANOS at additive cost.

This paper studies a modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve R and interest-bearing cash C. The risky sleeve is a static 50/50 combination of equal-weight growth/technology and defensive income/value ETF baskets; the target is future R-C return, with the cash leg earning the contemporaneous cash rate. Two independent filters are tested. The slow-tail filter maps continuous compensation, rate-headwind, risk-premium-compression, and rate-path-stress states into a cash weight with a 30% material-trade gate. The V-shape filter is a fast crash brake based on continuous VIX, rate, credit, drawdown, and re-entry states. A fixed max-cash layer then uses the larger cash weight requested by either filter each day. On the 2017-2026 common window, the selected max-cash combination earns an 18.83% CAGR versus 16.62% for 100% R and reduces maximum drawdown from -33.59% to -18.05%. In the main walk-forward OOS window, the expanding combination earns 19.35% versus 17.59% for 100% R, with maximum drawdown of -22.05% versus -33.59%; the rolling version earns 18.50% with the same -22.05% drawdown. Post-2022 tests show lower drawdown but lower CAGR during a strong risky-sleeve rebound. The results support modular cash overlays as drawdown-control tools rather than standalone return-enhancement claims; fully real-time variable re-screening and multiple-testing-adjusted inference remain future work.

We study a pair of nearly-unstable Hawkes processes coupled through a one-directional, or triangular, cross-excitation: the first component evolves autonomously and excites the second, but not conversely. Each component is self-exciting through a heavy-tailed memory kernel, and the two kernels are allowed to have different tail indices, so that the limiting components exhibit genuinely different degrees of roughness. As the system approaches criticality, we prove that the suitably rescaled intensity vector converges weakly to the unique solution of a coupled system of stochastic Volterra equations of rough-volatility type. The first limiting component is autonomous, while the second is driven both by its own noise and by an inherited noise transmitted from the first component through an effective cross-kernel. This cross-kernel is the convolution of the two limiting Mittag-Leffler kernels and therefore combines the two memory structures. As a consequence, we obtain a short-time cross-decorrelation law: although the two components are coupled, their functional correlation vanishes at small time scales at an explicit polynomial rate. This time-dependent correlation distinguishes the limit from independent rough processes and from classical bivariate rough models with constant Brownian correlation.

We provide a brief primer for the idea behind formalising hierarchical causality in the context of complex systems. Here actors are not simply agents. Actors instantiate causation classes. Agents implement local dynamics in given levels or organisation in a given system. Hierarchical causality then describes how actor-level roles constrain, select, and organise agent-level behaviour across levels. The system then necessarily requires three additional structures. First, causation classes to abstract a given form of causal influence that an actor instantiates. Second, aggregation operators to move across the levels. Third, discrete event-time maps are required because the system comprises events, and the relation between local event counts and any global clock must be specified. Our formulation here is purposefully simple and discrete.

We present two explicit rational formulae for Bachelier, or normal, implied volatility. The formulae take the option price, forward, strike, and expiry as inputs and return the implied normal volatility without iteration. They follow the branch structure of LFK-4, but use the simpler near-the-money variable given by the absolute forward-strike difference divided by the tail time value, avoiding a logarithm and a small-argument Taylor branch in that region. LFK-2026 is the accuracy-oriented formula and approximates reciprocal absolute standardized moneyness directly in the far tail. LFK-2026C keeps the same shifted out-of-the-money rational tail approximation, but splits the near-the-money branch two low degree rationals. In double precision tests both remain close to machine accuracy, while LFK-2026C is the faster scalar implementation on the current benchmark mix.

Advances in quantum computing challenge the hardness assumptions underlying widely deployed public-key cryptography in blockchain systems. Although post-quantum cryptography (PQC) standards are emerging, understanding quantum risk remains fragmented across research, engineering, governance, and investment communities. This demo presents Quantum Futures Interactive, a live interdisciplinary demonstration combining educational visualization, participatory interaction, and demonstrative post-quantum artifact generation using a toy LWE-based construction. Participants engage in a structured seven-stage interaction flow covering quantum threat education, sentiment capture, technology prioritization, infrastructure tradeoff exploration across simulators and QPUs, and artifact generation. The system integrates distributed trust concepts and sustainability-aware infrastructure considerations within an interactive decision framework.

U.S. Treasury yields are central to global asset pricing but are noisy and subject to policy uncertainty, supply-demand forces, and behavioral effects, exposing forecast users to downside risk. We formulate yield curve forecasting as a decision problem under distributional uncertainty and propose a distributionally robust ensemble framework that combines parametric factor models with machine-learning forecasts. A factor-augmented Dynamic Nelson-Siegel model captures yield-curve dynamics, while Random Forests model nonlinear interactions. Robust forecast combinations penalize tail risk and improve out-of-sample performance across maturities. The framework supports disciplined $DV01$-based interest-rate risk management for corporate, institutional and balance-sheet decision makers.