Papers

This paper develops a latent-state framework for recovering borrower-level posterior beliefs in credit-risk analysis. Creditworthiness and financial fragility are represented as latent dimensions, while observed borrower scores follow a finite Gaussian mixture model and default depends on the latent profile. Borrower-specific probabilities of default are obtained by averaging profile-specific default probabilities over the posterior distribution of latent states. A joint Expectation–Maximization procedure is used to estimate the mixture structure and the profile-specific default probabilities from observed score–default pairs. After estimation, predictive posterior beliefs are computed using the observed scores alone, thereby preserving the information available before default realization. A controlled simulation experiment evaluates the recovery of structural parameters, posterior beliefs, and borrower-level probabilities of default. Posterior distributions are interpreted as points on the probability simplex, and their recovery is assessed using both conventional error measures and information-geometric divergences. The results provide a controlled benchmark for studying the interaction between latent economic structure, posterior uncertainty, and credit-risk prediction.

Bayesian inference in compound loss models must often be repeated across policies, market scenarios, and prior specifications. Outside conjugate cases, this may require repeated numerical integration or Markov chain Monte Carlo (MCMC). We formulate this problem as amortized posterior approximation and construct a conditional Wasserstein generative adversarial network conditioned on sufficient statistics, prior mean and coefficient of variation, and mixture weights of prior families. Notably, a single shared generator is able to approximate the posterior laws of both the Poisson intensity and the Pareto shape parameter under mixtures of Gamma, inverse-Gaussian, and lognormal priors. We assess the approximation by simulation-based calibration and by comparisons with analytical posteriors, deterministic quadrature, and extensive MCMC simulations. In an application to data on extreme natural catastrophe losses, we produce rolling one-year posterior predictive distributions, and examine the effects of heavy-tailed severity and prior-family uncertainty on aggregate tail risk.

We extend a residual-learning hybrid credit scoring framework (logistic regression scorecard plus a gradient-boosting correction on its residuals, decomposed at each prediction into an interpretability ratio $\rho(x)$ that measures the share attributable to the linear branch) along three axes: an East African empirical instantiation on the Zindi Financial Inclusion in Africa data (Kenya, Rwanda, Tanzania, Uganda); a fairness audit at the granularity of the framework's three interpretability regions; and a thin-file segmentation analysis. On the Taiwan Credit Default benchmark retained for continuity, the calibrated hybrid attains AUC $= 0.776$ ($\Delta\mathrm{AUC} = +0.057$ vs.\ standalone logistic regression, $+0.001$ vs.\ standalone XGBoost), reduces Brier Score by 23%, and concentrates the highest-default-rate borrowers (69.5%) in the fully interpretable region. On Zindi, the calibrated hybrid attains AUC $= 0.869$ ($\Delta\mathrm{AUC} = +0.015$ vs.\ LR, $p < 0.001$; $-0.004$ vs.\ XGBoost), cuts Brier from $0.158$ to $0.085$ (a 46% reduction), and replicates the regional routing pattern. The fairness audit detects severe routing into the opaque ML-driven region along socioeconomic axes: rural respondents by 18 percentage points relative to urban, primary-or-less-educated by 32 points relative to secondary-and-above, and Ugandan respondents by 22 points relative to Kenyan, while gender shows essentially no routing disparity. The audit pipeline surfaces subgroup-routing violations that aggregate fairness metrics miss, in a form directly usable by African central-bank supervisors of digital credit.

Evaluating customer creditworthiness is crucial for retail banking operations, as it impacts marketing strategies, customer relationship management, and credit risk control. Traditional methods often struggle to capture complex temporal dependencies and extract pertinent information from customer data, crucial for accurate risk assessment. Specifically, they fail to differentiate between temporal patterns indicative of credit risk and those reflecting general customer behavior or preferences, leading to suboptimal risk predictions. In this study, we introduce the Disentangled Temporal Dependencies Variational Autoencoder (DTD-VAE), an advancement over conventional VAE, designed to disentangle temporal dependencies and distinguish credit risk-related features from past customer preferences. The feature inference module of the DTD-VAE incorporates an autoregressive temporal dependency learning mechanism that adeptly captures the temporal dependencies among latent variables, enriching the model's comprehension of the inherent data structure. Furthermore, the feature generative module utilizes an element-wise gating mechanism that assigns independent weights to each dimension of the expert models, enabling a finer-grained disentanglement of latent variables, particularly those relevant to credit risk prediction. Extensive experiments on six real-world datasets demonstrate that the proposed framework consistently outperforms existing methods, achieving performance gains of 3.2%-4.86% in ROC-AUC and 6.41%-9.71% in Accuracy Ratio.

We develop natural parametric (NatPar) insurance as the natural next step from natural-catastrophe (NatCat) modelling: the same hazard-exposure-vulnerability-finance machinery, with a parametric index made contractual in place of indemnity loss adjustment. Our aim is practical - a standard approach inspired by how the catastrophe-insurance industry already operates, not another optimal-contract criterion. This delivers two payoffs. First, it fixes how reporting is formulated: NatPar contracts are reported in the native NatCat language (annual average loss, EP/AEP/OEP curves, return-period levels), complemented with two-sided basis-exceedance diagnostics (BEP+/-) elevated to the central status the EP curve holds for losses - the canonical distributional view of basis risk, not a supplementary number. Second, the same standard shows how the tail is reallocated between insuree and insurer. A frost case study yields the central result: it is about time, not average. Holding a contract AAL-neutral, the bounded payout cannot follow the unbounded exposure tail, so equalising the mean separates over- and under-payment across return periods: the insuree gains at short horizons while the insurer sheds the deep tail past a crossover of several decades. This reverses under tail dependence - when regions reach extremes jointly, bounded payouts stack and the insurer reabsorbs the deep tail.

Credit risk models increasingly need to combine predictive accuracy with transparent explanations and auditable fairness constraints. Logistic regression remains attractive because its coefficients are easy to interpret, but it can miss nonlinear structure. Flexible models can improve prediction, but their explanations are often post-hoc and may not describe the decision rule itself. We introduce $\texttt{findr}$, short for flexible, interpretable deep regression, a semi-structured framework for binary credit risk modelling that decomposes the logit into an interpretable structured component and an orthogonal neural residual. The orthogonalisation separates coefficient-based effects from residual nonlinear variation, while an in-processing Wasserstein penalty mitigates group disparities by comparing score distributions during training. The framework also includes diagnostics that measure the structured component's contribution to logit variation, decision agreement, and local directional consistency. We evaluate $\texttt{findr}$ in a simulation study and on eight public credit datasets using score-level accuracy-fairness frontiers. The results show that $\texttt{findr}$ behaves close to logistic regression when the signal is approximately linear, while recovering much of the predictive gain of neural models when nonlinear structure is relevant. The diagnostics identify when coefficient-based explanations remain close to the full fitted model and when residual variation must also be examined. These findings support semi-structured modelling as a practical way to make performance, fairness, and interpretability trade-offs explicit in credit risk decisions.

We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the matrix-Dyson-equation framework (MDE), with numerical evidence supporting Tracy-Widom edge universality for every fixed $\rho<1$ of the exponential decay correlations; the degenerate limit $\rho\to1^-$ reduces to a symmetrized Volterra operator, connecting to the singular-value cascade identified in a companion BBP analysis. For power-law correlations $dt\sim t^{-\gamma}$, we identify $\gamma_c=1/2$ as the critical point for divergence of the bulk fourth-moment, while $\gamma=1$ marks the breakdown of the flatness condition governing the MDE edge analysis. We prove the fourth-moment transition exactly and find numerically that the self-consistent edge varies smoothly across $\gamma=1$, with no evidence of a kink or discontinuity.

Physical crash probabilities recovered from option prices depend on a pricing kernel and on a risk-neutral distribution that finitely many bid and ask quotes do not identify. For a power utility investor, we characterize the pairs of physical crash probability and expected loss below the crash threshold that the quotes admit; the boundary of this set is the physical crash frontier. Both coordinates are ratios of moments, yet when the index is bounded above the closed set is convex, and under an interior regularity condition second-order cone programs compute it exactly at the benchmark risk aversion of two. In a decade of weekly S&P 500 cross sections, the quotes beyond the two puts nearest a 10 percent decline shrink the range of admissible crash probabilities by about 80 percent, yet its upper end remains two to three times its lower end. Under strict quote slack and the interior-mass condition stated below, removing the cap without further tail control drives the lower bounds on crash probability and unconditional shortfall to zero for risk aversion above one. A vanishing probability far in the right tail inflates the normalizing moment while every quote remains inside its spread. In this setting, a positive floor requires additional tail information, supplied here by the support cap.

Financial stability rests on the premise that distress is largely idiosyncratic and therefore diversifiable: when one institution errs, the rest of the system absorbs the shock. That premise fails when many decision-makers depend on the same infrastructure. Agentic AI systems, which take consequential actions rather than only emitting predictions, are becoming such a substrate, and the binding concern shifts from the model risk of a single deployment to the systemic risk of the population. We develop this account in six mathematical settings. Chapter 1 recasts the PD/LGD/EAD decomposition of expected loss as an expected-harm identity and introduces a set-valued containment-risk measure; under a lever-assignment axiom that review cannot intercept an irreversible action, no non-preventive control satisfies a coherent tail constraint. Chapter 2 lifts this to a fleet sharing a foundation model: the shared model is a non-diversifiable common exposure whose expected-shortfall floor holds however large the fleet grows, and a percolation threshold governs contagion. Chapter 3 recasts these dynamics as a marked, Hawkes-excited jump diffusion, identifying the robust stress problem with a time-consistent entropic risk measure. Chapter 4 treats runtime guardrails as partially observed stochastic control, giving an observability trichotomy, a detection floor, and, under commit exogeneity, a runtime-impossibility corollary. Chapter 5 makes the adversary a player, yielding an underinvestment wedge proportional to systemic reach. Chapter 6 makes capability a state variable in an arms race. One claim runs through all six: the systematic component of agentic risk cannot be diversified, detected away, or reversed, and only ex-ante structural prevention moves it.

Emile Durkheim's Suicide: A Study in Sociology (1897) predates much of the statistical machinery that quantitative modellers now take for granted. Yet, working with sparse and imperfect observational data, Durkheim repeatedly arrives at practices that remain remarkably relevant to modern modelling. This paper revisits Suicide from the perspective of quantitative risk modelling, not for its substantive conclusions, but for the reasoning by which Durkheim reached them. His approach illustrates how careful definition, common sense, logical investigation, scepticism toward convenient explanations, and close attention to what the data can and cannot support—all of which must precede, and can often substitute for, statistical sophistication. The broader lesson is simple: good modelling begins not with technique, but with understanding the problem, interrogating the evidence, and reasoning carefully about what it can actually tell us.

Costly LLM features matter only if calibration lets them affect the forecast. We document a failure of this link in a next-day risk study of two broad-market funds. Full-history scoring preceded the 2022 calibration. Calibration then set all four LLM weights to zero. The 856 later scores therefore could not affect the evaluation. We call this calibration-induced degeneracy. Allowing signed weights reactivated all four mappings. None improved forecasts after familywise correction. By contrast, a near-zero-cost headline count reduced SPY variance-forecast loss by 0.001720 (95 percent familywise interval: [0.000719, 0.002830]). The cheap baseline is therefore a critical diagnostic. We propose a calibration-viability checkpoint. Fit the mapping, perturb the feature over prespecified calibration values, and require a meaningful forecast response before acquiring holdout features. The check uses no holdout outcomes. Here, it would have stopped the paid full-history inference phase.

We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection–golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.

Optimal execution (OE) in multi-asset settings involves complex interactions across assets, particularly through shared capital constraints during portfolio rebalancing. While existing models capture cross-impact and portfolio-level dynamics, they largely overlook the role of explicit cash constraints along the execution trajectory. As a result, the feasibility of execution strategies under limited capital remains poorly understood. In this paper, we extend the classical Almgren-Chriss framework to incorporate intertemporal constraints on expected cash consumption, requiring that the expected cumulative cash spent does not exceed a prescribed budget at every trading period. We show that the resulting multi-asset OE problem can be equivalently formulated as a quadratically constrained quadratic program (QCQP), and further establish that it admits a convex representation under mild conditions. This provides a tractable framework for analyzing execution strategies under dynamic capital constraints. Through controlled synthetic experiments, we show that the proposed cash constraints qualitatively alter OE schedules toward cash-feasible sell-first executions as the constraints become tighter. Furthermore, evaluations in an out-of-sample agent-based market simulator demonstrate that our method substantially reduces peak cash drawdown while maintaining implementation shortfall comparable to existing execution strategies. Our results highlight the importance of explicitly modeling financial feasibility in multi-asset execution and provide a foundation for bridging theoretical OE models with practical capital constraints.

We develop parametric Entropic Value-at-Risk (EVaR) portfolio optimization for tempered stable Lévy returns. We derive portfolio cumulant-generating functions and weight-dependent admissible moment-generating-function domains under two multivariate constructions: a multivariate normal tempered stable approach and an independent component factorization. These expressions allow portfolio EVaR to be evaluated from fitted asset- or component-level parameters without repeated portfolio-level distribution fitting. We construct minimum-EVaR portfolios and two entropic reward–risk portfolios. We test the portfolios in a rolling 2000 to 2026 out-of-sample U.S. sector ETF allocation. In this universe, several entropic portfolios have higher realized Sharpe ratios than their matched CVaR portfolios or standard allocation benchmarks.

Credit decisioning is a high-stakes task in which model outputs must be accurate and explainable to support compliant decisions. Although modern credit risk models such as eXtreme Gradient Boosting (XGBoost) and Graph Neural Networks (GNNs) improve predictive performance, their explanations are often too technical for stakeholders creating communication gaps that can shape approvals, denials, and fairness judgments. We examine whether Large Language Models (LLMs) can serve as explanation layers that translate post-hoc explanation artefacts into stakeholder-appropriate risk narratives. Using Freddie Mac single-family loan-level data, we develop three pipelines: standard tabular (XGBoost + SHAP), and two with alternative data, a pure network-based (GNN + GNNExplainer), and a bimodal one (combining tabular and network data). We generate narratives with three LLM configurations: a small fine-tuned LLM (Gemma 3 4B), a large fine-tuned LLM (DeepSeek R1 70B), and a zero-shot commercial LLM (Gemini 2.5). Explanation quality is evaluated through automated checks across all pipelines and a human study of bimodal explanations comparing credit risk professionals and non-professionals on eight decision-relevant dimensions. We have three main findings. First, the pipeline accounts for higher variance in evidence-grounding scores than the language model, meaning that the binding constraint on explanation quality is the evidence representation, not the model used. Second, the explanation narratives reliably name the influential factors but are less reliable when stating the direction of influence, which may be consequential for adverse-action communication. Finally, professionals apply stricter evidentiary standards than non-professionals. We discuss implications for the governance of risk models, including deployment considerations and the value of domain-aligned LLMs in regulated credit settings.

We present in this article a non-parametric value-at-risk (VaR+CVaR) algorithm that remains accurate for an arbitrarily large number of underlying positions. The algorithm solves the two inherent problems of VaR estimation. First, past history is not directly applicable to the future, but all predictions of the future are based on the past. Second, VaR estimation is equivalent to modeling a single corner of a high-dimensional space (the corner where all bets lose simultaneously). The algorithm only uses mathematical methods that strictly do not degrade in accuracy at high-dimensions. Historical data are then directly incorporated with all high-dimensional relationships present, without manipulation. We test the algorithm with an ensemble of 500 portfolios with random positions across 49 distinct liquid futures of different expiries (VIX, equity indexes, gov. bonds, rates, energy, metals, livestock, agriculture, and softs). All VaR estimations are performed strictly blind to the future. The median portfolio rate of loss exceeding the 99% confidence daily VaR estimate is between $1.0\pm0.1$% depending on algorithm input parameters. 68% of portfolios have a rate of loss exceeding 99% VaR between $1.0\pm0.3$%, and 95% of portfolios between $1.0\pm0.5$%.

This paper develops a theoretical framework for signed optimal transport. A global flatness measure induced by the continuum transport equation serves as the regularizer. We examine transport networks from a harmonic analysis perspective, prove the existence and uniqueness of the optimal coupling in the variational problem, and provide an algorithmic scheme that guarantees lossless information transport under bi-marginal constraints. To bridge theory with practice, we design an empirical analysis framework for the resulting optimal estimators, which is sufficiently general to accommodate both time-series and panel-structural analyses of the network, owing to the intrinsic invariance properties of locally compact abelian groups.

Financial returns are heavy-tailed, and accurate tail risk estimation is central to portfolio risk management. Modern neural generators sample by pushing a simple base distribution through a learned map, and for training stability that map is built from Lipschitz components. This is the binding constraint: a Lipschitz map of a Gaussian is sub-Gaussian, so heavier-tailed targets admit no exact match at any finite Lipschitz constant. The Monge–Ampère equation ties the Brenier map's local distortion to the density ratio $f/(g\circ T)$, so a deeper trough in the target density requires a higher-gain map and yields a higher-variance estimator. The argument needs only bounded distortion, so it covers normalizing flows, flow matching, GANs, and diffusion samplers alike. Semi-Discrete Optimal Transport (SDOT) relaxes the map's regularity rather than the source's tail class. Its power diagram gives every training observation a cell holding exactly $1/N$ of the source measure, and tail observations are reached by crossing a cell boundary rather than by stretching. Our primary experiment sweeps severity over a calibrated Merton jump-diffusion spanning kurtosis 94 to 1,679. SDOT holds tail ratios at $0.85$–$0.94$ with cross-seed standard deviations below $0.025$, while every learned generator either compresses the tails or inflates them with a variance that grows alongside. Further experiments carry the result to real S&P~500 returns and to a 21-year backtest, where SDOT gives the best risk-adjusted market-neutral strategy under CVaR optimization (Sharpe $0.70$, max drawdown $-2.60\%$, against $0.40$ for the next-best generator).

Decentralized lending lacks a credit bureau: a borrower's capacity to repay must be inferred entirely from public on-chain activity, without income verification or a liability record. This paper presents zLend, a deployed cash-flow underwriting framework that reconstructs a wallet's daily balance history from raw token transfers and derives short-duration repayment-capacity signals from it. The reconstruction is performed twice per wallet, once restricted to a fixed stablecoin basket and once over all fungible transfers, on the premise that a wallet's total token holdings and its liquid, spendable balance are distinct quantities whose conflation misprices risk. From each series we derive liquidity coverage against a fixed loan size, cash-flow volatility and regularity, a drawdown-and-recovery statistic adapted from quantitative finance, and a recurring-counterparty detector that identifies salary-like payment cadence from transfer timing alone. The two views are then compared: a wallet with large aggregate holdings whose stablecoin reserve rarely covers the loan size is flagged as a liquidity mismatch irrespective of total wealth. We specify the pipeline formally, document the golden-master methodology used to verify a cross-language production migration to numerical tolerance 1e-9, and characterize the tier function's parameter sensitivity with an independent reimplementation validated to exact agreement (78 of 78 field assertions) against the deployed system's reference fixtures. Tier assignment is governed predominantly by the reference loan size, with four of six reference wallets changing tier across loan sizes from USD 10 to USD 25,000; the drawdown and coverage criteria bind on disjoint wallets, so neither subsumes the other; and no criterion in the tier rule is inert. zLend is deployed in production, informing real lending decisions via third-party API integrations.

Mobile money has widened financial access across Sub-Saharan Africa and enlarged the surface for money-laundering and terrorism-financing (ML/TF) activity in ecosystems dominated by high-volume, low-value transactions. Rwanda is a case in point: several million active mobile-money users, telecom-led wallets on the MTN and Airtel networks, and a Financial Intelligence Centre (FIC) supervising transaction streams whose scale exceeds static rule-based monitoring. This paper develops and evaluates a transaction-monitoring framework aligned to the Rwandan AML/CFT regime under (i) extreme class imbalance (~0.1% prevalence), (ii) scarce and delayed labels, and (iii) bounded investigator capacity. Using SAML-D, a synthetic dataset of 9,504,852 transactions with 17 laundering typologies, we engineer account-centric behavioural features (rolling velocity, net-flow directionality, counterparty diversity, burstiness) and benchmark supervised classifiers (Logistic Regression, Random Forest, LightGBM), unsupervised anomaly detectors (Isolation Forest, Local Outlier Factor), a dense autoencoder, and a late-fusion meta-learner. Evaluation is operational: PR-AUC, recall at a calibrated ~90%-precision point, recall at top-K%, and alerts per 10,000. On the chronologically held-out test period, LightGBM attains PR-AUC = 0.0469, capturing 64 laundering cases at precision ~0.89 with 0.51 alerts per 10,000; the fusion stacker reaches PR-AUC = 0.0477 at precision ~0.91 and 0.46 alerts per 10,000, recovering 59 true positives. We map score bands to Rwanda-relevant analyst workflows and STR/SAR escalation, and outline a staged path from synthetic prototyping to real-data validation with the National Bank of Rwanda and FIC. The contribution is operational: a governance-aware pipeline and evaluation protocol calibrated to the constraints of an African mobile-money regulator, not a new algorithm.

Investors interpret social disclosures from a risk perspective, yet relevant information can reach them through channels that differ sharply in regulatory enforcement and materiality: SEC filings, sustainability reports, or financial reports. We analyse how social disclosure via each channel relates to idiosyncratic risk. Studying S&P 1,500 constituents, we distinguish between initiated and continued disclosure along the three disclosure channels. We find first-time disclosure of social issues via SEC filings is related to increased idiosyncratic firm risk, highlighting that unexpected information is published. Continuous disclosure of social issues is related to lower idiosyncratic risk for sustainability and financial reports, which is in line with the literature. The SEC filing effect is robust for downside idiosyncratic risk measures, the separation of social disclosure into human capital, product liabilities, and stakeholder engagement, and for propensity score matching. Our findings suggest that the risk impacts of sustainability disclosure depend on the newness of information and disclosure channels.

This paper develops a unit-consistent actuarial framework for pricing capped cumulative temperature-index insurance under long-range dependence and stochastic variability. Daily temperature anomalies are modeled as increments of fractional Brownian motion evaluated at an operational time generated by the integral of a stationary normalized Cox–Ingersoll–Ross process. We show that the stochastic time change preserves stationarity and the long-memory covariance decay of the increments while introducing additional variability through the random operational clock. The cumulative temperature index admits a conditionally Gaussian representation, which leads to an exact conditional exponential kernel for capped stop-loss contracts and ensures existence of the entropic premium for every positive risk-aversion parameter. Consequently, valuation reduces to an outer Monte Carlo expectation over the accumulated CIR time, avoiding fractional Brownian path simulation and covariance-matrix construction. We further establish monotonicity properties of the premium with respect to risk aversion and conditional volatility. An empirical illustration based on Chicago temperature data shows that both long memory and stochastic time change can materially affect insurance premiums relative to conventional Brownian and fractional Brownian benchmarks, with the Hurst parameter playing an important role in valuation uncertainty. The proposed framework therefore provides a tractable approach for incorporating persistent dependence, stochastic variability, and bounded insurance losses into climate-index pricing.

We study stress-scenario generation for systems driven by multivariate heavy-tailed risk factors. Within regions where several financial losses are simultaneously extreme, stress analysis concerns both the conditional law of the risk factors and the most plausible configurations producing those losses. We show that both are governed by the same limiting tail law. Preserving its measure recovers rare-event probabilities and scaled conditional stress laws, while misspecifying extremal dependence distorts some regular joint-stress probability. Its density governs reverse-stress optimization, whose maximizers identify the most plausible stress configurations. To exploit this common structure in finite samples, we develop SSGEN (Self-Similar Generative Estimation), which learns extremal dependence from intermediate exceedances and extrapolates to rarer levels using a Pareto radial component. Even when the target event is absent from the sample, we establish convergence rates for the generated conditional law, and data-driven reverse-stress solutions.

Shariah-compliant equity screening provides a transparent setting in which institutional rules determine who may own a stock. A binary label identifies current eligibility but not whether the feasible investor base is fragmented across standards or close to changing. We define this instability as classification uncertainty and formalize its investor-base consequence through permitted investor mass. In a 1999-2024 CRSP-Compustat panel of 13,188 securities classified under seven researcher-emulated Shariah rulebooks, screening-rule disagreement and proximity to active boundaries rank next-month screen-implied transitions. U.S. Fama-MacBeth diagnostics do not support an unconditional equal-weighted permission premium, and a September 2023 DJIM/S&P methodology change produces no robust matched repricing. The central event evidence uses 25 official Securities Commission Malaysia lists. The 410 inclusions already trading before the preceding review have positive but imprecise matched returns. Applying the pre-event turnover floor yields 295 inclusions with 1.76 percentage points over $[0,10]$ trading days ($p_{\mathrm{date}}=0.008$; $p_{\mathrm{wild}}=0.017$) and 2.25 points over $[0,20]$ ($p_{\mathrm{date}}=0.018$; $p_{\mathrm{wild}}=0.035$). Leave-one-date-out, first-inclusion-only, and mid-review placebo checks are supportive, although a joint 20-day pre-event test rejects. Ownership and demand-pressure diagnostics do not identify a unique marginal buyer or clean causal demand shock. The evidence supports treating classification risk as a portfolio-monitoring state. Official Shariah permission is associated with price effects in a recognized local market among sufficiently tradable securities; formal eligibility alone is insufficient.

Signed graphs provide an effective architecture for portraying a system in which cooperation and conflict coexist. Emerging from the concept of balance in psychological sciences, they have found applications across several domains. Financial markets are one such example that can be modeled using signed networks, where assets exhibit correlations in price movements. During periods of systemic risk, such a signed financial network shows a loss of balance, which has been consistently demonstrated. Here, we explore how this structural imbalance is distributed across scales within the financial network, revealing its mesoscopic origin. Adopting the framework of structural balance theory, we use a measure of polarization based on triadic motifs to investigate the distribution of structural imbalance across varying sectoral scales. We analyze the temporal evolution of global polarization and its sectoral constituents using longitudinal data derived from the S&P 500 index. By decomposing global polarization into intra-sectoral and inter-sectoral constituents, we show that structural imbalance arises predominantly from interactions between sectors rather than within them during periods marked by systemic risk. We employ randomization protocols to confirm that observed imbalance configurations are statistically significant and not artifacts of lower-order interactions. We derive a regression equation demonstrating that the variance in global polarization is well explained by macroeconomic variables, indicating that low levels of global polarization during economic crises are driven by compounding pressures from supply chain disruptions and inflation uncertainty. Collectively, these findings provide a quantitative framework for understanding how localized sectoral conflicts propagate across the financial network and contribute to large-scale structural instability during periods of economic crisis.

Financial institutions are delegating consequential decisions to agentic AI systems that decompose goals, coordinate models and tools, and act with little oversight. Yet agentic AI governance in FinTech is under-investigated. We argue the binding governance constraint is not capability but verifiability. We define the Verifiability Gap as the shortfall between the verification delegated authority demands and the explainability and reproducibility retained after a decision. It is indexed to a verifier, evidentiary standard, and audit lag. We develop a multilevel governance theory for agentic AI and test its mechanisms in three studies over nine model versions, from a three-billion-parameter local model to a commercial frontier system. Study 1 shows that provider releases alter historical financial actions, and that the controls replay needs belong to the provider: the frontier model rejects temperature, top_p and top_k outright and exposes no random seed. Under the tightest controls each endpoint allows, a local model reproduced 320 of 320 executions, hosted models 319 of 320 and 959 of 960. Study 2 shows that orchestration is a latent policy layer. Architecture changes final actions, and no execution record repeated in any configuration at any scale. The frontier model reproduces its own actions more often than the local ones, its record no better, and loses a comparable share of its differentiation. Capability buys a higher starting point, not auditability. Study 3 shows two deterministic credit-model versions each reproduce their current action perfectly, yet the current cannot recover a historical one. We conceptualize reproducibility as a governance profile, not a scalar, yielding evidence-contingent delegation: authority is defensible only while retained evidence substantiates its exercise. Beyond finance, the framework extends to other high-stakes domains requiring auditability.

The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.

We develop a behavioural model of bank run exposure in a paycheck-to-paycheck economy with loss averse depositors. Income is received through demand deposits, and consumption ratcheting embeds reference dependence in a parsimonious asset-pricing framework. We show that sufficiently high subjective bad-state probabilities endogenously increase liquidity demand and generate equilibrium stress states supporting bank runs. These states define a Bank Run Exposure State Space and yield a martingale representation for exposure dynamics. A proof-of-concept empirical implementation using Call Report data constructs bank-level exposure proxies from funding and lending composition. A regression-weighted composite measure modestly improves fit relative to a retail-share benchmark, with stronger amplification among small banks and during the post-Silicon Valley Bank (SVB) collapse period. The framework highlights how behavioural liquidity demand alters equilibrium reserve holdings and can crowd out productive lending.

We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading applied to the peer's expected loss. To justify the bargaining formulation relative to a standard fixed-weight weighted-sum optimization problem, we provide an axiomatic characterization showing that the Nash bargaining solution satisfies properties well suited to voluntary P2P insurance contracting in small pools. We establish the existence and uniqueness of the optimal contract and derive first-order characterizations for the full-, partial-, and zero-reinsurance regimes. To address subgroup formation, we develop computationally tractable sufficient conditions that rule out viable coalitional deviations, both with and without price fairness. Our numerical study investigates the impact of price fairness and pool size on the optimal contract and agents' welfare. Price fairness reduces dispersion in risk allocations and certainty-equivalent loadings among peers. Regarding pool size, welfare need not increase monotonically, highlighting that risk-pool expansion depends not only on diversification but also on the evolution of bargaining power.

Climate perils are linked through event ordering and state-dependent propagation, features not fully captured by joint loss distributions alone. This paper develops a Cascading Climate Risk Network (CCRN) for multi-peril reinsurance that separates calendar-scale climate conditioning from within-event propagation on a directed acyclic graph (DAG). The model combines complementary-log-log triggering hazards with bounded severity activation, mapping physical states to insured losses via a capacity-bounded demand-surge transformation. For fixed shocks, the event-scale cascade reaches a unique finite-step closure. Monotone comparative statics provide a pathwise upper-corner loss bound over rectangular stress sets, yielding a transparent contract-level stress-testing guarantee under common aleatory inputs. Comprehensive numerical experiments, including copula and Bayesian-network benchmarks, sensitivity analyses, and uncertainty propagation, demonstrate that while central layer prices remain robust across matched-marginal dependence structures, far-tail and high-layer behaviors differ materially. Directional propagation, annual event frequency, and dependence strength emerge as the principal risk drivers. The study provides a controlled synthetic verification of the proposed architecture.