The probabilistic reading of the cumulative accuracy profile (CAP) has a long industry lineage. Falkenstein, Boral and Carty (2000) state, in discrete form, that the default rate at a score percentile equals the portfolio average rate times the local slope of the power curve; van der Burgt (2008, 2019) formalizes this as the continuous identity $p(D\mid x) = p_D\, dy/dx$ and imports the continuous form as a working fact; Tasche (2009) analyzes the resulting calibration method; Voloshyn and Voloshyn (2023) substitute Bayes' theorem, $f(x\mid D)=p(D\mid x) f(x)/p_D$, into the area integral and write the Gini as a functional of the calibration curve. The slope itself is already in the lineage (van der Burgt's $dy/dx$ is the ratio of the two cumulative differentials), but it enters as a cited working fact, never as Bayes' theorem. We make that identification explicit and draw out its consequences. First, the CAP slope is Bayes' theorem in cumulative coordinates: the standardized PD it recovers is the posterior probability rescaled by the prior. The weight of the paper then falls on two results this reading unlocks. The odds form places the weight of evidence (the log of the likelihood ratio, i.e. the Bayes factor) and the information value inside one geometry (the weight of evidence at a point is the log of the ratio of the "bad" and "good" CAP slopes). The accuracy ratio, Somers' $D_{xy}$, and the Gini $(2A-1)/(1-p_D)$ are revealed as one number computed three ways. Run in comparison mode (realized outcomes against model claims), the same identity recovers the reliability diagram in cumulative coordinates, with the sign of the gap between the empirical and model-implied Gini coefficients as a calibration diagnostic. A worked five-band example carries every identity in discrete form, and a kernel-density example extends them to the continuous case.

We analyze distributions of historic S&P500 multi-day returns, for the number of days of accumulation from 20 to 120. With the increase of the number of days of accumulation, we observe clear tempering of power-law tails toward a seemingly finite value. To explain this phenomenon, we employ a model that produces a "capped Inverse Gamma" stationary (steady-state) distribution for stochastic volatility which, in turn, produces a "tempered Student-t" distribution for returns. We then employ Jones-Faddy-like symmetry breaking mechanism that produces a "tempered Skew-t" distribution. This distribution provides rather good fits to the distributions of accumulated multi-day S&P500 returns, which exhibit symmetry breaking between gains and losses -- as reflected by positive mean and negative skew. Tempered Skew-t fits are also consistent with near perfect linear dependence on the number of days of accumulation of the mean values and, even more so, of the variances (mean squared realized volatility) of the distributions.

This paper presents a reproducible synthetic benchmark comparing a computational planner, an agent-based market, and a hybrid meta-market within a common simulated economy. The benchmark incorporates input-output production networks, heterogeneous firms, capacity constraints, endogenous prices, welfare metrics, structural shocks, adversarial stress testing, and information-reporting experiments. Across training, holdout, and adversarial scenarios, the planner consistently achieves lower welfare losses than the decentralized alternatives. The main contribution is methodological rather than ideological. While the benchmark demonstrates a falsifiable framework for comparing economic coordination mechanisms, it does not establish the empirical superiority of planning. Several design choices mechanically favor the planner, including informational asymmetries, incomplete market representation, and simplified institutional assumptions. The results should therefore be interpreted as validation of a synthetic experimental architecture and as a prototype for future research. The paper concludes by outlining a validation agenda based on empirical calibration, structural holdouts, sensitivity analysis, uncertainty quantification, mechanism-design tests, and independent replication.

An integrated and extendable approach for stress-testing loan portfolios is presented, which includes both a loan production component and a credit risk component. In this approach, we simulate a completed portfolio using realistic loan parameters and distributional assumptions. Thereafter, we generate the uncertain cash flow history of these loans within a multistate probabilistic framework. We illustrate our approach using a simulation-based study, though the approach can be fit to real-world data. Such a simulation-based approach is ideal for stress-testing since it allows for evaluating a range of conditions. From these completed loans, we compute portfolio-level credit risk metrics, e.g., default and loss rates. Stress scenarios are introduced by varying the loan parameters accordingly within a broader Monte Carlo setup, thereby resulting in a range of portfolios. A classical approach to stress-testing does not typically integrate loan production or embed the correlation structure amongst risk metrics. In our approach, we integrate the forecasting of risk metrics with receipt-generation. Given data, the loan parameters within our extendable approach can be dynamically modelled as functions of input variables using any applicable technique. Overall, our approach can render predictions that are more dynamic and flexibly tuned, which can enhance stress-testing practices within any bank.

This paper complements and extends Doldi, Frittelli and Maggis, Collective completeness and pricing-hedging duality, Math. Finan. Econ. 19, 757-784 (2025), by studying collective pricing and hedging when admissible risk exchanges form a finitely generated convex cone. The collective First Fundamental Theorem of Asset Pricing and the collective pricing-hedging duality are extended to this setting. A key contribution is a closedness result showing that no collective arbitrage implies the closedness of the aggregate feasibility cone combining infinite-dimensional trading opportunities with finite-dimensional exchanges. The paper also proves that no-collective-arbitrage prices for vectors of contingent claims form a relatively open convex set. Finally, strong collective replicability is introduced and shown to be equivalent to price uniqueness. This leads to an enhanced collective Second Fundamental Theorem of Asset Pricing, providing equivalent characterizations of collective completeness and strong collective completeness in terms of the uniqueness of the collective equivalent martingale measure. We highlight that several core aspects of the theory are substantially altered when exchanges belong to a convex cone rather than a vector space.

This paper studies the macroeconomic dynamics of climate policy in a multi-sector dynamic general equilibrium model with renewable and non-renewable energy, sector-specific capital adjustment frictions, household energy demand, and endogenous fossil resource dynamics. The central mechanism is that decarbonization requires reallocating energy use and installed capital: fossil energy demand can contract immediately, while renewable capacity and abatement adjust only gradually. The analysis delivers four results. First, gradual policy implementation sharply reduces transition costs: relative to immediate implementation, gradual emissions caps improve welfare by 2.26 percentage points under comprehensive regulation and by 5.06 percentage points under firm-only regulation. Second, renewable energy subsidies and non-renewable energy taxes support renewable capital accumulation and reduce, but do not eliminate, the welfare cost of front-loaded tightening. Third, sectoral coverage changes the welfare ranking across implementation speeds. Firm-only regulation performs better under gradual implementation because it shields utility-relevant household energy services, but becomes nearly as costly as the carbon-price-only transition under immediate implementation. Fourth, endogenous fossil exploration and stock-dependent extraction costs transmit climate policy into lower extraction, fewer discoveries, and a declining shadow value of reserves, providing a structural mechanism for stranded fossil assets. The results show that deep decarbonization can be achieved at substantially lower macroeconomic cost when policy manages the speed and incidence of energy-capital reallocation.

Using average vehicle speed data in 10-minute increments at the Traffic Message Channel (TMC) location level, along with precise crash timing and location information, we analyze driving behavior around five Florida stadiums before and after NFL and NBA regular season games from 2015 to 2019. We find no evidence of emotional driving following NBA games, but strong and consistent effects following NFL games, concentrated in predicted-close games that end in disappointing home-team losses -- combining high pre-game suspense with negative outcome valence. These games are associated with significant increases in average vehicle speed within 3 km of stadiums during the first post-game hour, dissipating with increasing time and distance from the stadium. Average vehicle speed increases by up to 3 mph relative to predicted-close games that ended in a win -- an effect several times larger than the typical game day versus non-game day speed differential. Overall, our results highlight how the combination of sustained suspense and negative outcome valence in close sporting contests can spill over into risky post-game driving behavior, underscoring the behavioral and public safety implications of affective cues in large-scale sporting events.

Previous studies conclude that intermediaries account for a large share of exports. Using Spanish firm-level data, we show that many firms classified as intermediaries are either manufacturer-owned export arms that ship their parent firms' products or vertically integrated firms that control design, production, and distribution and predominantly export goods sold under their own brands. Once we exclude these export arms and vertically integrated firms, the share of intermediaries in exports in our sample falls by about 70%. We also show that pure intermediaries differ markedly from export arms and vertically integrated firms along key firm and export dimensions.

Some firms export their own products directly, others rely on intermediary firms to export on their behalf, and still others both export their own products and intermediate exports for other producers. To explain this heterogeneity, we develop a model in which firms differ along two dimensions: manufacturing capability and commercial capability. Manufacturing capability lowers the marginal cost of producing a variety, whereas commercial capability lowers the variable cost of reaching foreign customers. Different combinations of these capabilities generate the different types of firms observed in export markets: direct exporters, indirect exporters, pure intermediaries, and hybrid firms. The model predicts that commercially capable intermediaries are matched with more manufacturing-capable producers, and that more commercially capable intermediaries export a broader set of varieties. We provide suggestive evidence for these predictions using Spanish firm-level export data.

This volume develops a knowledge theory of capital for economies in which productive capacity increasingly resides in software, data, models, routines, expertise, platforms, organizations, commons, and public epistemic infrastructure. Beginning from Adam Smith's theory of labour, stock, specialization, and market extent, it asks what changes when knowledge becomes stock-like, mobile across forms, scalable, governable, recombinable, and imperfectly visible in accounting. The book introduces knowledge-bearing stock as the central object and analyses how it is generated, converted into governable form, deployed, improved through feedback, enclosed or shared, measured, impaired, and used as input to future production. It distinguishes embodied, disembodied, institutionalized, commons, and public knowledge forms and develops concepts such as first conversion, cognitive enclosure, feedback capture, dark capital, and expected knowledge loss. The argument is conditional and testable: modern wealth depends not only on capital accumulation, but on how productive knowledge is governed.

Legal precedents protect computer code as copyrightable expression. They have enabled centralized digital platforms -- operating from corporate servers that hold all user data -- to construct private governance regimes through the interaction of copyright, contract, and technical architecture: people who create virtually all platform value must surrender effective copyright control through Terms of Service agreements as a condition of participation. In contrast, grassroots platforms consist of cryptographically-identified people operating their networked smartphones independently of any server or global resource; each person holds their own data on their own device, with no third party in possession or intermediation. Here, we define the notion of a \textit{digital speech act} -- a deliberate volitional act by a person of cryptographically signing personal content with the person's private key, carried out on the person's own device -- through which the person simultaneously establishes attribution, accountability, and authorship over the signed content. We contend that (\ia) digital speech acts qualify for copyright protection under existing U.S.\ precedent: \textit{Burrow-Giles} locates authorship in volitional creative choices despite mechanical or algorithmic processes, \textit{Feist} supplies the minimal-creativity threshold, and persistent device storage satisfies the Copyright Act's fixation requirement; (\ib) the digital social contract underlying grassroots platforms preserves this copyright by design -- signed content cannot be unbundled from its signature, and the full provenance chain accumulates as content is forwarded -- so that ownership and possession coalesce in the person; and (\ic) copyright in digital speech acts is a prerequisite for digital sovereignty and democratic self-governance.

Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

This paper studies the optimal portfolio, consumption, and endogenous early retirement problem within a benchmark tracking framework by incorporating a new relative performance evaluation. In this framework, the investor maximizes expected lifetime consumption utility while managing the maximum wealth shortfall relative to a benchmark, with shortfall-management costs that may differ before and after retirement. Mathematically, the problem is a hybrid stochastic control problem involving both regular controls and an optimal stopping time, in which the running maximum process records the investor's largest benchmark shortfall. We introduce an auxiliary reflected state process and establish an equivalent hybrid stochastic control problem. By proving the convex duality theorem, we technically transform the original problem into a two-dimensional pure optimal stopping problem with state reflection. This enables us to characterize the geometric structure of the stopping set and derive the feedback-form optimal retirement boundary, as well as optimal portfolio and consumption policies. Analytical examples and numerical simulations reveal a two-stage structure with more conservative investment and more aggressive consumption after retirement. Driven by the retirement option, the expected largest shortfall risk follows a pronounced U-shaped pattern with respect to wealth. Shortfall management costs, labor income, and leisure preference significantly influence retirement timing, investment, and consumption.

How should recommender systems be designed when recommendations shape access to scarce, short-lived opportunities? We study this question in a production setting: Timee, Japan's largest platform for spot work, where workers favorite job templates and receive notifications when firms post shifts from those templates. Maximizing predicted favoriting can generate misdirected concentration: recommendations accumulate on popular templates that create few viable job openings, while templates with unmet labor demand receive too little exposure. We design exposure-control mechanisms for favorite-list management, reallocating template exposure based on posting activity and unfilled capacity. The proposed recommender, thresholded eligibility control (TEC), is fully parallelizable and suitable for large-scale digital platforms. In simulations calibrated to Timee data, TEC raises the per-round job-finding rate from 57.6% to 70.0%. A prefecture-level randomized field experiment increases realized matches and exposure per active template, reduces the share of low-exposure templates, and improves impression-level favoriting and downstream matching.

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.

This paper studies how market informedness affects market makers' profitability in a computational market environment with heterogeneous learning agents. We develop an agent-based market model in which market makers differ in their information sets and inventory-risk aversion, prices form endogenously, fundamental values evolve exogenously, and market-taker order flow follows a state-dependent self-exciting process. The model provides a controlled computational laboratory for analyzing the interaction between informed trading, adverse selection, price discovery, and liquidity provision. We establish finite-horizon stability properties of the market-taker order-flow process and solve the market-making problem using multi-agent reinforcement learning with centralized training and decentralized execution. The results show that informed market order flow is particularly harmful when aggregate market informedness is low, exposing market makers to severe adverse-selection risk. However, as market informedness increases, market-maker profitability displays an overall upward trend despite local non-monotonicities arising from complex market dynamics and stochastic learning. This suggests that the price-discovery benefits of informed trading can offset its adverse-selection costs. The findings contribute to computational economics by showing how agent heterogeneity, endogenous price formation, and learning-based liquidity provision jointly shape market outcomes.

Cryptocurrencies are increasingly adopted as investment assets, making their interactions with traditional financial markets central to cross-asset diversification and systemic risk. This paper studies the integration of cryptocurrencies, fiat currencies, and S&P500 equities using a balanced panel of 381 assets from October 2017 to February 2024. We combine rolling correlation networks, community structure, market-specific and system-wide Turbulence Indices, and VAR-based connectedness analysis to examine how market stress, network structure, and shock transmission vary across financial regimes. The results show that cross-asset integration is episodic. In calm periods, the three asset classes remain relatively segmented, whereas under stress, local clustering increases, modular separation weakens, and communities become more compositionally mixed across asset classes. Connectedness analysis further shows that regime shifts alter the structure of transmission rather than simply increasing spillover magnitudes. In high-turbulence states, fiat-market turbulence becomes the dominant propagation channel, while network clustering and modularity play a greater role in transmitting forecast uncertainty. These findings support the interpretation of network structure as an emergent, state-dependent transmission layer rather than a persistent exogenous driver of turbulence. The results highlight the need for regime-aware risk monitoring, since full-sample connectedness estimates can understate the cross-asset coupling that emerges precisely when diversification benefits are most fragile.

We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal T^{op} \to \mathbf{Prob},$ we consider the associated conditional expectation transport functor $\mathcal E \circ F : \mathcal T^{op} \to \mathbf{Ban},$ and the canonical distortion $dF(i) := (\mathcal E \circ F)(i)(1),$ which measures the failure of constant functions to be preserved under non-measure-preserving transitions. Motivated by the multiplicative transport structure of $dF$, we introduce a simplicial distortion operator defined recursively on the nerve $N_\bullet(\mathcal T)$ of the time category. This construction describes recursively accumulated transported distortions along composable chains of morphisms and leads naturally to a notion of holonomy along loops. We interpret non-trivial holonomy as a global inconsistency invisible at the level of individual transitions, analogous to the Aharonov-Bohm effect in physics. This yields a notion of AB arbitrage, in which arbitrage opportunities arise from global loop effects rather than local price discrepancies. We further introduce simplicial admissibility conditions ensuring that recursively accumulated distortions remain integrable, and show how non-trivial holonomy can be translated into predictable self-financing trading strategies through executable loop dynamics. This establishes a connection between categorical holonomy structures and economically realizable arbitrage. The framework developed here suggests a global and homological perspective on arbitrage theory, in which market inconsistencies are encoded by recursively accumulated simplicial distortions and their holonomy along loops in the underlying time category.

Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation of a normalised correlated Gaussian random vector $|x\rangle=\vec{x}/\lVert\vec{x}\rVert$, $\vec{x}\sim\mathcal{N}(0,Σ)$, and its exponentiation $|e^{\vec{x}} \rangle= e^{\vec{x}}/\lVert e^{\vec{x}}\rVert$. When an $O(\mathrm{polylog} N)$-gate-depth quantum data loader for the covariance matrix $Σ\in\mathbb{R}^{N\times N}$ is available, preparing $|x\rangle$ and $|e^{\vec{x}}\rangle$ require $\widetilde{O}\left(\frac{\lVertΣ\rVert_F}{λ_{\max}}κ^{1.5}\right)$ and $\widetilde{O}\left(\lVert\vec{x}\rVert\frac{\lVertΣ\rVert_F}{λ_{\max}}κ^{1.5}\right)$ elementary gate depth respectively, where $\lVertΣ\rVert_F$, $λ_{\max}$, $κ$ denote the Frobenius norm, maximal eigenvalue, and condition number of $Σ$. Motivated by financial applications, we provide an end-to-end resource analysis when $\vec{x}$ represents a sample path of a Riemann-Liouville or standard fractional Brownian motion, or of a stationary fractional Ornstein-Uhlenbeck process. As a concrete example, we construct the quantum state encoding the rough Bergomi variance process and analyse the extraction of the integrated variance via quantum amplitude estimation. Under specific conditions, the dependence of $\lVertΣ\rVert_F/λ_{\max}$ and $κ$ on $N$ is small, and subcubic complexity in $N$ is achieved, indicating a quantum advantage over classical Cholesky-based sampling methods. To our knowledge, this constitutes the first quantum algorithmic framework for the amplitude encoding of exponentiated Gaussian processes, providing foundational primitives for quantum-enhanced financial modelling.

Commercial fusion energy requires frameworks to assess both the scientific and economic viability of a wide variety of fusion concepts. Inspired by the Lawson criterion's ability to universally describe fusion energy gain, a generalized framework is developed to determine the economic gain of fusion power plants. The model exploits temporal equilibrium, and engineering and cost parameters normalized to the energy capture surface. The derived criteria for economic gain are therefore independent of the power plant's absolute power, impartial to the particulars of its fusion technology, and can be applied to any fusion confinement concept. The derivation of the economic gain factor, $Q_{econ}$, results in nonlinear equations with ten controlling normalized design parameters ranging from fusion power density and surface component lifetime to energy fluence, price of energy, and component efficiency and cost. These ten controlling parameters are varied over a wide range to provide high-level insights in design, finance and operational tradeoffs that improve the prospects for economically viable fusion energy.

An elementary Recurrent Neural Network that operates on p time lags, called an RNN(p), is the natural generalisation of a linear autoregressive model ARX(p). It is a powerful forecasting tool for variables displaying inherent seasonal patterns across multiple time scales, as is often observed in energy, economic, and financial time series. The architecture of RNN(p) models, characterised by structured feedbacks across time lags, enables the design of efficient training strategies. We conduct a comparative study of learning algorithms for these models, providing a rigorous analysis of their computational complexity and training performance. We present two applications of RNN(p) models in power consumption forecasting, a key domain within the energy sector where accurate forecasts inform both operational and financial decisions. Experimental results show that RNN(p) models achieve excellent forecasting accuracy while maintaining a high degree of interpretability. These features make them well-suited for decision-making in energy markets and other fintech applications where reliable predictions play a significant economic role.

We consider the problems of estimation and optimization of utility-based shortfall risk (UBSR). We extend UBSR to cover possibly unbounded random variables. We cover prominent risk measures such as entropic risk, expectile risk, Value-at-Risk, and quadratic risk as special cases of the UBSR. In the context of estimation, we derive non-asymptotic bounds on the mean absolute error (MAE) and the mean-squared error (MSE) of the classical sample-average approximation (SAA) estimator for the UBSR. In the context of optimization, we derive an expression for the gradient of UBSR under a smooth parameterization. We propose a gradient estimator for the UBSR and derive non-asymptotic bounds on MAE and MSE for this estimator. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) optimization algorithm and derive non-asymptotic bounds on the convergence rate of our SG algorithm for optimizing UBSR under three objectives, namely, strongly convex, convex and non-convex. Finally, we conduct experiments on financial applications to demonstrate the performance of our proposed UBSR estimation and optimization algorithms.

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary local stochastic maximum principle, applied to log-wealth, tailored to Epstein-Zin utility, and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for equilibrium investment and consumption policies. The strength of our approach is further illustrated by two special cases: (i) in the power utility setting without consumption, we obtain the same one-to-one correspondence as in Fu and Zhou [22] under exactly the same assumption, but without invoking the dynamic programming principle in Espinosa and Touzi [16]; and (ii) in the power utility setting with both investment and consumption, we strengthen the correspondence result of Fu [18], by proving a genuine one-to-one relation in the BMO space, where both the equilibrium strategy and the associated BSDE components belong to BMO.

We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We introduce two novel integral operators that are consistent with the Hamilton-Jacobi-Bellman equation for the resulting two-dimensional singular control problems. The first operator involves integrals where the integrator is the control process of the two-dimensional process $(X,I)$ or $(X,S)$; the second operator concerns integrals where the integrator is the running infimum or supremum process itself. Using these definitions, we prove a general verification theorem for problems involving two-dimensional state-dependent running costs, costs of controlling the process, costs of increasing the running infimum (or supremum) and exit times. Finally, we apply our results to explicitly solve an optimal dividend problem in which the manager's time-preferences depend on the company's historical worst performance.

We establish a first- and second-order approximation for an infinite dimensional limit order book model in a single (critical) scaling regime where market and limit orders arrive at a common time scale. With our choice of scaling we obtain non-degenerate first- and second-order approximations for the price and volume dynamics. While the first-order approximation is given by a coupled ODE-PDE system, the second-order approximation is described in terms of an infinite-dimensional stochastic evolution equation driven by a cylindrical Brownian motion. The driving noise processes exhibit a non-trivial correlation in terms of the model parameters. We prove that the evolution equation has a unique solution and that the sequence of standardized limit order book models converges weakly to the solution of the evolution equation. The proof uses a non-standard martingale problem. We calibrate a linearized model to market data and explain how our model can be used for deriving confidence intervals of portfolio liquidation values.