We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the baseline risk measure. We prove continuity in the neighborhood radius and provide a stable large-radius behavior. In Banach lattices, the approach leads to a convex risk measure and under separability of the space, a dual representation through a penalty term based on an inf-convolution taken over a Gelfand integral constraint. We also relate our veraging to aggregation at the distribution and quantile levels of payoffs, obtaining dominance and coincidence results. Numerical illustrations are conducted to verify calibration and sensitivity.

We study the nonlinear chaotic dynamics in a system of linear oscillators coupled by social network links with an additional stratification of oscillator energies, or frequencies, and supplementary nonlinear interactions. It is argued that this system can be viewed as a model of social stratification in a society with nonlinear interacting agents with energies playing a role of wealth states of society. The Hamiltonian evolution is characterized by two integrals of motion being energy and probability norm. Above a certain chaos border the chaotic dynamics leads to dynamical thermalization with the Rayleigh-Jeans (RJ) distribution over states with given energy or wealth. At low energies, this distribution has RJ condensation of norm at low energy modes. We point out a similarity of this condensation with the wealth inequality in the world countries where about a half of population owns only a couple of percent of the total wealth. In the presence of energy pumping and absorption, the system reveals features of the Kolmogorov-Zakharov turbulence of nonlinear waves.

Portfolio backtesting is the primary tool for evaluating investment strategies before deployment, yet practitioners implicitly assume that different engines produce identical results for the same strategy. we formalise implementation risk, the systematic divergence in backtested portfolio metrics arising solely from differences in how engines implement the same logical strategy, and propose four metrics grounded in metrology to quantify it: engine sensitivity, implementation uncertainty interval, divergence amplification factor, and conclusion stability index. we execute 15 benchmark strategies through five independent open-source engines on 30 non-overlapping stratified asset buckets comprising 180 s&p 500 stocks under four transaction-cost regimes. at zero cost, all five engines agree exactly (maximum divergence 0.000%), isolating transaction-cost implementation as the sole source of disagreement. under nonzero costs, divergence is structured and predictable (spearman rho = 0.93 with cost intensity), remaining below 0.75 percentage points for most strategies but reaching 3.71% for high-turnover rotation strategies. source-code forensics uncovered seven previously undocumented defects across three engines, abstracted into a five-category failure-mode taxonomy. all engines agree on the sign of every performance metric (conclusion stability index = 1), so implementation risk does not alter investment decisions for the strategies studied but introduces measurable ambiguity in performance attribution. code and benchmark data are publicly available.

How much macroeconomic information is contained in a single input-output table? We feed FIGARO 64-sector symmetric tables into DEPLOYERS, a Darwinian agent-based simulator, producing genuine out-of-sample GDP forecasts. For each year, the model reads one FIGARO table for year N, self-organizes an artificial economy through evolutionary natural selection, then runs 12 months of autonomous free-market dynamics whose emergent growth rate predicts year N+1. The I-O table is the only input: no time series, no estimated parameters, no expectations formation, no external forecasts. We present five results. First, a 9-year Austrian panel (2010-2018) using 12-seed ensembles produces MAE of 1.22 pp overall; for five non-crisis years, MAE falls to 0.42 pp -- comparable to the best professional forecaster (WIFO: 0.48 pp). A Swedish 9-year panel independently confirms this accuracy (normal-years MAE 0.80 pp). Second, cross-country portability is demonstrated across 33 of 37 tested FIGARO countries with zero parameter changes. Third, a German 9-year panel reveals systematic +3.7 pp positive bias from export dependency -- an informative negative result pointing to multi-country network simulation as the natural extension. Fourth, a COVID-19 simulation demonstrates the I-O structure as a shock propagation mechanism: a 19-month timeline produces Year 1 GDP -4.62% vs empirical -6.6%. Fifth, emergent firm size distributions match European Commission data without micro-target calibration. These results establish the I-O table as serving a dual purpose: structural baseline engine and dynamic shock propagation mechanism. Since FIGARO covers 46 countries, the approach is immediately portable without retuning parameters.

Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of diversification correspond to notions of risk aversion. We focus on the classical distinctions between weak and strong risk aversion, and consider diversification preferences for pairs of risks that are identically distributed, comonotonic, antimonotonic, independent, or exchangeable, as well as their intersections. Under a weak continuity condition and without assuming completeness of preferences, diversification for antimonotonic and identically distributed pairs implies weak risk aversion, and diversification for exchangeable pairs is equivalent to strong risk aversion. The implication from diversification for independent pairs to weak risk aversion requires a stronger continuity. We further provide results and examples that clarify the relationships between various diversification preferences and risk attitudes, in particular justifying the one-directional nature of many implications.

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power-law kernel. After suitable rescaling the price-volatility process converges weakly to a rough Heston model. Our convergence result is stronger than previously established ones that have either focused on light-tailed kernels or the convergence of integrated volatility process. The key is to establish the tightness of the family of rescaled volatility processes. This is achieved by introducing a new methods to establish the $C$-tightness of càdlàg processes based on the classical Kolmogorov-Chentsov tightness criterion for continuous processes.

When designing product rankings, online retailers and platforms choose which outcome to maximize: revenues from commissions or markups, the number of transactions, or consumer welfare. These objectives need not align, creating potential trade-offs. This paper studies how rankings differ between objectives and quantifies the resulting trade-offs. I provide descriptive evidence showing that lower-priced and high-utility alternatives gain more demand when ranked higher, suggesting that ranking them higher increases transactions and consumer welfare but may decrease revenues. To quantify these trade-offs, I develop and estimate a structural demand model based on the search and discovery framework of Greminger (2022) and construct rankings for each objective. The results show that these counterfactual rankings all increase consumer welfare, transactions, and platform revenues relative to a neutral benchmark and the status quo, and that trade-offs between these rankings are limited.

Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencies and quantile levels, enabling the quantile-frequency analysis (QFA) of nonlinear serial dependence. This paper introduces some spectral measures based on the quantile periodogram for diagnostic checks of financial time series models and for model-based discriminant analysis. A simulation-based parametric bootstrapping technique is employed to compute the $p$-values of the spectral measures. The usefulness of the proposed method is demonstrated by a simulation study and a motivating application using the daily log returns of the S\&P 500 index together with GARCH-type models. The results show that the QFA method is able to provide additional insights into the goodness of fit of these financial time series models that may have been missed by conventional tests. The results also show that the QFA method offers a more informative way of discriminant analysis for detecting regime changes in financial time series.

This paper introduces a transformative framework for managing path-dependent financial risk by shifting from traditional distribution-centric models to a geometry-based approach. We propose the SigSwap as a new regulatory instrument that allows market participants to decompose complex risk into terminal price law and the underlying texture of the price path. By utilising the mathematical properties of the path-signature, we demonstrate how previously unmodellable risks, such as lead-lag dynamics and flash-crash spiralling, can be converted into transparent and linear risk factors. Central to this framework is the introduction of Signature Expected Shortfall, a risk metric designed to capture toxic path geometries that traditional methods often overlook. We also present a proactive monitoring system based on the Temporal Exposure Profile, which utilises anticipatory learning to detect potential liquidity traps and geometric decoupling before they manifest as realised volatility. The proposed methodology offers a rigorous alignment with global regulatory mandates, specifically the Fundamental Review of the Trading Book (FRTB), by providing a consistent bridge between physical stress-testing and risk-neutral hedging. Finally, we show that this algebraic approach significantly reduces computational complexity, enabling real-time, high-frequency risk reporting and capital optimisation for the modern financial ecosystem.

We introduce a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution, costs, and P&L. The book state is projected onto a tractable representation based on spread and volume imbalance, enabling robust estimation from market data. Event timing is calibrated to reproduce the fine-scale temporal structure of real markets, revealing a pronounced mode at exchange round-trip latency consistent with simultaneous reactions and latency races among participants. We further incorporate a feedback mechanism that accumulates signed trade flow through a power-law decay kernel, reproducing both concave market impact during execution and partial post-trade reversion. Across several stocks and strategy case studies, the simulator yields realistic behavior where profitability becomes highly sensitive to execution parameters. We present the approach as a practical recipe: project, estimate, validate, adapt, for building realistic limit order book simulations.

For simultaneous independent events with finitely many outcomes, consider the expected-utility problem with nonnegative wagers and an endogenous cash position. We prove a short support theorem for a broad class of strictly increasing strictly concave utilities. On any fixed support family and at any optimal portfolio with positive cash, summing the active first-order conditions and comparing that sum with cash stationarity yields the exact identity \[ \fracλ{K_{\ell}^{(U)}}=\frac{1-P_{\ell,A}}{1-Q_{\ell,A}}, \] where $P_{\ell,A}$ and $Q_{\ell,A}$ are the active probability and price masses of event $\ell$, $λ$ is the budget multiplier, and $K_{\ell}^{(U)}$ is the continuation factor seen by inactive outcomes of that event. Consequently, after sorting each event by the edge ratio $p_{\ell i}/π_{\ell i}$, the exact active support is the eventwise union of the single-event supports, and this support is independent of the utility function. The single-event utility-invariant support theorem is already explicit in the free-exposure pari-mutuel setting in Smoczynski and Miles; the point of the present note is that the simultaneous independent-events analogue follows from the same state-price geometry once the right continuation factor is identified.

This paper studies firms' optimal response to a trade liberalization shock in terms of export and product innovation both theoretically and empirically. We find that trade liberalization, namely China's WTO accession, reduces trade cost and promotes export, which in turn incentivizes firms to innovate as the marginal benefit of innovation for exporting firms is higher than that for non-exporting firms. In addition, as a firm starts to innovate, it predicts to have a higher probability of moving to a better productivity state and can save the entry cost of innovation in the future, resulting in additional dynamic benefits. Such an innovation-promotion effect is an unintended consequence of trade liberalization.

This paper examines how age at migration affects cultural assimilation by studying convergence in gender role attitudes between immigrants and the UK-born population. Although cultural values are central to policy debates about integration and social cohesion, most work on migration timing focuses on economic outcomes, leaving effects on values and beliefs far less explored. We address this gap by combining a sibling design with a distributional framework for measuring attitude convergence. Using the UK Household Longitudinal Study, we compare siblings within the same family who arrived in the UK at different ages, exploiting within-family variation to identify the causal effect of childhood exposure to host-country norms. To measure convergence, we compare the full distributions of ordinal survey responses to questions on gender norms for immigrants and locals. Our distance metric is the Total Variation (TV) distance between response distributions. TV has a clear policy-relevant interpretation: it equals the worst-case difference in mean responses over all bounded scoring rules. We then use our estimates to construct two measures of how migration timing changes this distance. The first asks how large the immigrant-UK-born TV distance would be if every immigrant had arrived at birth, and compares it to the observed distance. The second is a marginal measure that asks how the distance changes under a small uniform shift in arrival ages. Our results show that if all immigrants had arrived at birth, the cultural distance between immigrants and locals would decrease substantially, and that marginal increases in migration age incrementally widen this gap. Overall, the findings highlight the importance of early-life exposure in shaping cultural beliefs and provide a robust, broadly applicable framework for quantifying convergence in survey responses.

Anti-money laundering (AML) systems are important for protecting the global economy. However, conventional rule-based methods rely on domain knowledge, leading to suboptimal accuracy and a lack of scalability. Graph neural networks (GNNs) for digraphs (directed graphs) can be applied to transaction graphs and capture suspicious transactions or accounts. However, most spectral GNNs do not naturally support multi-dimensional edge features, lack interpretability due to edge modifications, and have limited scalability owing to their spectral nature. Conversely, most spatial methods may not capture the money flow well. Therefore, in this work, we propose LineMVGNN (Line-Graph-Assisted Multi-View Graph Neural Network), a novel spatial method that considers payment and receipt transactions. Specifically, the LineMVGNN model extends a lightweight MVGNN module, which performs two-way message passing between nodes in a transaction graph. Additionally, LineMVGNN incorporates a line graph view of the original transaction graph to enhance the propagation of transaction information. We conduct experiments on two real-world account-based transaction datasets: the Ethereum phishing transaction network dataset and a financial payment transaction dataset from one of our industry partners. The results show that our proposed method outperforms state-of-the-art methods, reflecting the effectiveness of money laundering detection with line-graph-assisted multi-view graph learning. We also discuss scalability, adversarial robustness, and regulatory considerations of our proposed method.

Scientific innovation often comes from researchers who pivot across disciplines. However, prior work found that established researchers face productivity penalties when pivoting. Here, we investigate the consequences of pivoting at the beginning of a research career -- doctoral admissions -- when the benefits of importing new ideas might outweigh the switching costs. Using applications to all PhD programs at a large research-intensive university between 2013-2023, we find that pivoters (those applying to programs outside their prior disciplinary training) have lower GPAs and standardized test scores than non-pivoters. Yet even conditional on these predictors of admission, pivoters are 1.3 percentage points less likely to be admitted. Examining applicants who applied to multiple programs in the same admissions cycle provides suggestive evidence that the admissions pivot penalty is causal. This penalty is significantly smaller for applicants who secure a recommendation from someone within the target discipline. Among those admitted and enrolled, pivoters are 12.9 percentage points less likely to graduate and do not show superior publication performance on average or at the tail. Our results reveal the substantial costs of disciplinary pivoting even at the outset of research careers, which constrain the flow of new ideas into research communities.

How do entrepreneurs act on their beliefs when probabilities of outcomes are unknown but subjectively perceived? We theorize that two distinct dimensions of ambiguity attitudes influence entrepreneurial action: ambiguity aversion - the unwillingness to bear ambiguity - and ambiguity sensitivity - how individuals discriminate between different levels of perceived chances of success. The second dimension determines how much entrepreneurs adjust their actions based on new information - a distinct aspect that cannot be captured by ambiguity aversion alone. Our theory suggests that entrepreneurs with different growth orientations have different ambiguity attitudes as compared to employees. Using incentivized measures from a large-scale survey, we find that incorporated entrepreneurs exhibit lower ambiguity aversion than employees, indicating that they are more willing to act under ambiguity. Distinctively, unincorporated self-employed individuals show higher ambiguity sensitivity, indicating that their actions are more responsive to changes in their beliefs. These patterns persist after controlling for risk attitudes, optimism, cognitive ability, and demographics. Our results highlight the distinct impacts of ambiguity aversion and ambiguity sensitivity on entrepreneurial actions.

As data is an essential asset for any DeFi application, selecting an oracle is a critical decision for its success. To date, academic research has mainly focused on improving oracle technology and internal economics, while the drivers of oracle choice on the client side remain largely unexplored. This study addresses this gap by gathering insights from leading DeFi protocols, uncovering their rationale for oracle selection and their preferences regarding whether to outsource or internalize data-request mechanisms. Data are collected from founders, C-level executives, and oracle engineers of 32 DeFi protocols, whose combined total value locked (TVL) exceeds 55% of the oracle-using DeFi segment. The study leverages a one-time mixed-method survey, using tailored question paths for in-house versus third-party oracle users. Quantitative answers are summarized, compared across groups, and examined through Spearman rank-order correlations to explore pairwise associations among evaluation dimensions, while open-ended responses are inductively coded into keywords and broader themes to triangulate common selection motives and switching challenges. Insights support the view that protocol choices are tied to technological dependencies, in which the immutability of smart contracts amplifies lock-in, hindering agile switching among data providers. Furthermore, when viable third-party solutions exist, protocols generally prefer to outsource rather than build and maintain internal oracle mechanisms.

The payback period is unambiguously defined for conventional investment projects, projects in which a series of cash outflows is followed by a series of cash inflows. Its definition for nonconventional projects is more challenging, since their balances (cumulative cash flow streams) may have multiple break-even points. Academics and practitioners offer a few contradictory recipes to manage this issue, suggesting to use the first break-even point of the balance, the last break-even point of the balance, or the moment in time at which the cumulative sum of net cash inflows first exceeds the total sum of net cash outflows. In this paper, we show that the last break-even point of the project balance is the only definition of the payback period consistent with a set of economically meaningful axioms. An analogous result is established for the discounted payback period.

Urban mobility is undergoing rapid transformation with the emergence of new services. Mobility hubs (MHs) have been proposed as physical-digital convergence points, offering a range of public and private mobility options in close proximity. By supporting Mobility-as-a-Service, these hubs can serve as focal points where travel decisions intersect with operator strategies. We develop a bilevel MH platform design model that treats MHs as control levers. The upper level (platform) maximizes revenue or flow by setting subsidies to incentivize last-mile operators; the lower level captures joint traveler-operator decisions with a link-based Perturbed Utility Route Choice (PURC) assignment, yielding a strictly convex quadratic program. We reformulate the bilevel problem to a single-level program via the KKT conditions of the lower level and solve it with a gap-penalty method and an iterative warm-start scheme that exploits the computationally cheap lower-level problem. Numerical experiments on a toy network and a Long Island Rail Road (LIRR) case (244 nodes, 469 links, 78 ODs) show that the method attains sub-1% optimality gaps in minutes. In the base LIRR case, the model allows policymakers to quantify the social surplus value of a MH, or the value of enabling subsidy or regulating the microtransit operator's pricing. Comparing link-based subsidies to hub-based subsidies, the latter is computationally more expensive but offers an easier mechanism for comparison and control.

We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic terminal and running targets. Initially, we formulate the optimal trade execution task as a stochastic control problem with a finite-variation control process that acts as an integrator both in the state dynamics and in the cost functional. We then extend this problem continuously to a stochastic control problem with progressively measurable controls. By identifying this extended problem as equivalent to a certain linear-quadratic stochastic control problem, we can use established results in linear-quadratic stochastic control to solve the extended problem. This work generalizes [Ackermann, Kruse, Urusov; FinancStoch'24] from the single-asset setting to the multi-asset case. In particular, we reveal cross-hedging effects, showing that it can be optimal to trade in an asset despite having no initial position. Moreover, as a subsetting we discuss a multi-asset variant of the model in [Obizhaeva, Wang; JFinancMark'13].

Enterprise financial risk analysis aims at predicting the future financial risk of enterprises. Due to its wide and significant application, enterprise financial risk analysis has always been the core research topic in the fields of Finance and Management. Based on advanced computer science and artificial intelligence technologies, enterprise risk analysis research is experiencing rapid developments and making significant progress. Therefore, it is both necessary and challenging to comprehensively review the relevant studies. Although there are already some valuable and impressive surveys on enterprise risk analysis from the perspective of Finance and Management, these surveys introduce approaches in a relatively isolated way and lack recent advances in enterprise financial risk analysis. In contrast, this paper attempts to provide a systematic literature survey of enterprise risk analysis approaches from the perspective of Big Data and large language models. Specifically, this survey connects and systematizes existing research on enterprise financial risk, offering a holistic synthesis of research methods and key insights. We first introduce the problem formulation of enterprise financial risk in terms of risk types, granularity, intelligence levels, and evaluation metrics, and summarize representative studies accordingly. We then compare the analytical methods used to model enterprise financial risk and highlight the most influential research contributions. Finally, we identify the limitations of current research and propose five promising directions for future investigation.