In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk reduction can be achieved without relying on risk measurement and risk minimization. To this end, we propose a generalization of the numerical rank and the condition number of a matrix, specifically the return matrix in this application. This generalization considers the entire matrix spectrum instead of focusing only on the smallest eigenvalue, as the condition number does. The approach directly provides an order among a finite number of risky scenarios. Risk reduction is obtained by identifying the riskiest scenarios and reducing investment exposures corresponding to them. The validity of this theoretical proposal is supported by a comprehensive experiment performed on real data. The capacity of the proposed approach to effectively reduce risk is proven by measuring the variability of out-of-sample returns for benchmark portfolios-constructed by minimizing standard risk measures-compared to the strategy of reducing exposure in high-risk scenarios. Finally, preventing large losses with limited active management-thereby controlling the impact of transaction costs-not only reduces risk but also preserves the average return and, consequently, the portfolio's Sharpe ratio.

Despite many decades of research, economically grounded models that analyse energy consumption and energy-efficiency adoption within a unified framework remain underdeveloped. This article addresses this gap by proposing a model of consumption, investment, and energy-efficiency adoption under uncertainty. It develops new definitions of the rebound and backfire effects, and integrates their welfare implications into a model of optimal subsidy design. Macro-level technology diffusion and energy consumption across heterogeneous agents are also formalised. Explicit results for core objects are derived, including the adoption threshold and post-adoption strategies, and these are shown to depend on agent wealth, introducing a novel channel through which financial conditions influence technology-adoption decisions. An approximation scheme is proposed to estimate welfare implications explicitly. Adoption of energy efficiency is shown to be welfare improving in the main. A detailed case study of a representative German single-family home illustrates the theoretical results. Numerical analysis indicates that the subsidy policy effectively steers aggregate energy consumption.

This paper investigates two optimal insurance contracting problems under distributional uncertainty from the perspective of a potential policyholder, utilizing a Bregman-Wasserstein (BW) ball to characterize the ambiguity set of loss distributions. Unlike the $p$-Wasserstein distance, BW divergence enables asymmetric penalization of deviations from the benchmark distribution. The first problem examines an insurance demand model where the policyholder adopts an $α$-maxmin preference with Value-at-Risk (VaR). We derive the optimal indemnity function in closed form and study, both analytically and numerically, how the asymmetry inherent in BW divergence influences the optimal indemnity structure. The second problem employs a robust optimization framework, where the policyholder aims to secure robust insurance indemnity by minimizing the worst-case convex distortion risk measure while adhering to a guaranteed VaR constraint. In this context, we provide explicit characterizations of both the optimal indemnity and the worst-case distribution in closed form through a combined approach using the Lagrangian method and modification arguments. To illustrate the practical implications of our theoretical findings, we include a concrete example based on Tail Value-at-Risk (TVaR).

Recent disruptions at major maritime chokepoints have exposed the structural fragility of liner shipping networks. Existing indicators measure connectivity, but none quantify its structural vulnerability from a supply-side perspective. We propose the Maritime Connectivity Vulnerability Index (MCVI), capturing three dimensions mapped to distinct UNCTAD sources: low overall connectivity (LSCI), weak bilateral integration (LSBCI), and port infrastructure concentration (PLSCI). The index covers 185 economies over 2006-2025 using pooled fractional rank normalization and equal-weight aggregation from publicly available data. SIDS exhibit a mean vulnerability 0.234 points above non-SIDS economies, with the gap widening from 0.232 to 0.249 over two decades. A modest global decline of 4.2% is observed. Port concentration dominates for nearly 40% of economies (72 of 185), establishing infrastructure diversification as a distinct policy priority. Rankings are highly stable across alternative weighting schemes, normalization methods (Spearman rho = 0.97-0.999), and PCA-derived weights; Monte Carlo simulation (1,000 replications) confirms rho > 0.95 in every realization. External validation shows strong negative correlation with the World Bank Logistics Performance Index (rho = -0.61 across seven waves) and positive correlation with ad valorem maritime freight rates (rho = +0.32). Panel regressions reveal a vulnerability paradox whereby small trade-dependent economies are simultaneously the most trade-open and the most vulnerable. Pre-crisis MCVI predicts trade losses during the COVID-19 supply shock (rho = -0.25, p < 0.005), while the contrasting positive correlation during the 2008-2009 demand shock (rho = +0.23, p = 0.01) validates the supply-side specificity of the index.

This paper studies whether a lightweight supervised aggregator can combine diverse zero-shot large language model outputs into a stronger downstream signal for corporate disclosure classification. Zero-shot LLMs can read disclosures without task-specific fine-tuning, but their predictions often vary across prompt perspectives, model families, and confidence levels. I examine this problem with a multi-prompt framework in which three fixed zero-shot LLM classifiers read each disclosure from different financial perspectives and output a sentiment label, a confidence score, and a short rationale. A logistic meta-classifier then aggregates these outputs to predict next-day stock return direction. To reduce pretrained-model contamination, I restrict evaluation to a post-release sample of 9{,}860 U.S.\ corporate disclosures issued by large publicly traded firms between January 2025 and March 2026, after the release of the frozen base LLMs used in the experiment. Results show that the trained aggregator outperforms single classifiers, majority vote, confidence-weighted voting, a zero-shot LLM judge, and a FinBERT baseline. Balanced accuracy rises from 0.566 for the best single classifier to 0.606 for the trained aggregator. The gain is largest in mixed-signal disclosures where classifiers disagree. The results suggest that zero-shot LLM outputs contain complementary financial signals, while also showing that the strongest gains come from supervised aggregation rather than from zero-shot voting alone.

Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks, extending conventional (open-to-close) returns with intra-period high/low prices. Specifically, I construct candlestick-based estimators of regression parameters, including spot beta, by minimizing a quadratic risk under a fixed-k asymptotic framework. I then develop a feasible hypothesis testing procedure for spot betas with correct asymptotic size. Simulation results show that the proposed estimator reduces estimation risk relative to return-based estimators, especially in small samples, and the test achieves notably higher power. I apply the framework to assess the market neutrality of Bitcoin using 1-minute data on IBIT and SPY, finding deviations from neutrality, particularly in high-volatility periods.

Agricultural price volatility, driven by market dynamics and meteorological factors such as temperature and precipitation, poses challenges for sustainable finance, planning, and policy. This study analyzes the impact of climate on crop price volatility for soybean in Madhya Pradesh (India) and Illinois (US), rice in Assam (India), wheat in North Dakota (US), cotton in Gujarat (India), and corn in Iowa (US). Using CMIP6 climate projections from the Copernicus Climate Change Service, we examine historical climate patterns and evaluate two future scenarios: SSP2-4.5 (moderate) and SSP5-8.5 (severe). We estimate conditional price volatility using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model, and forecast this volatility with a Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors (SARIMAX) model that incorporates meteorological variables. Finally, we apply the Black-Scholes framework to evaluate the cost of put-option-based insurance, which provides protection to farmers against adverse price drops linked to climate change. Our results highlight the role of meteorological data in improving agricultural risk modelling, enabling better design of insurance mechanisms, price stabilization tools, and sustainable policy interventions under climate uncertainty.

Claims reserving is one of the most important actuarial tasks in non-life insurance modeling. There are several popular methods to perform claims reserving such as the chain-ladder (CL), the Bornhuetter--Ferguson (BF) or the generalized Cape Cod (GCC) methods. These methods have originally been introduced as deterministic algorithms, and only in a later step, they have been lifted to stochastic models allowing for analyzing claims prediction uncertainty. This holds true for the CL and the BF methods, but not for the GCC method. The purpose of this article is to close this gap and derive an analytical formula for the mean squared error of prediction (MSEP) of the GCC method.

The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time stochastic optimal control framework for intraday electricity trading using stochastic differential equations with drift terms ensuring mean reversion to deterministic forecast trajectories. Production follows a Jacobi diffusion, while prices follow an asymmetric jump-diffusion to reflect the heavy-tailed behavior observed in intraday markets. The framework accounts for realistic market features by incorporating gate closure and energy-based imbalance settlement over the delivery window, where the path-dependent imbalance cost is handled by state augmentation to preserve the Markovian structure. The value function is characterized via the dynamic programming principle by a three-stage sequence of two linear Kolmogorov backward equations and a nonlinear Hamilton-Jacobi-Bellman partial integro-differential equation. To solve this problem efficiently, we propose a monotone IMEX finite-difference scheme with operator splitting, semi-implicit linearization, and a differential formulation for the jump operator. Numerical experiments based on German market data indicate that, under the provided forecasts, the computed strategy outperforms the TWAP benchmark and approaches the perfect-foresight benchmark. Sensitivity experiments further show how jump intensity, delivery-window length, and trading horizon affect the trading policy and the resulting profit-and-loss distribution.

Renewed public attention on the identity of Bitcoin's pseudonymous creator has sharpened focus on the Satoshi overhang, commonly framed as a tail risk for bitcoin. This paper argues that the mechanical downside of a disposition is bounded well below the existential-loss framing, and that the terminal states most consistent with sixteen years of holder behavior are nonbearish for bitcoin's effective supply. The approximately 1.148 million BTC Patoshi position is analyzed on two tracks. For a purely wealth-maximizing holder, a three-scenario quantitative analysis (Appendix A) shows that bitcoin's current market depth is sufficient to absorb a patient multi-year liquidation at a cumulative price impact in the mid-single-digit to mid-double-digit percent range relative to counterfactual, with the central scenario clustering near 10 percent. The paper maps a decision space rather than identifying a unique modal outcome, assuming a holder whose profile is consistent with the sixteen-year record. Preference sets consistent with the record, including ideological non-intervention, privacy above all, satisficing, and myth preservation, favor continued dormancy terminating in a cryptographically enforced nonrecovery or destruction arrangement; preference sets favoring adversarial or wealth-maximizing action are possible but less supported. Across the plausible region of the decision space, the bear case is bounded and the terminal states most consistent with observed behavior are neutral to slightly positive for bitcoin's effective supply.

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler induced by the learned generator. Reliability therefore depends on two errors: sampler misspecification and finite-simulation error. We propose Sampler-Robust Optimization (SRO), which optimizes decisions against the worst-case sampler induced by perturbing the learned generator. This sampler-first formulation aligns with simulation-based decision pipelines and admits a sharpness-aware interpretation: it favors decisions whose performance is stable under generator perturbations, rather than merely under the nominal sampler. Under a coverage assumption, we show that the empirical worst-case objective provides a high-probability upper certificate for the true population objective, with finite-simulation error partially absorbed by the robustification used to guard against sampler misspecification. The framework accommodates generative models with or without explicit densities and admits efficient minimax procedures. Portfolio-optimization experiments show that SRO produces more stable decisions and improves out-of-sample performance under distribution shift.

Counterintuitively, the S&P 500 Index rose between January 1, 2022, and December 29, 2023, while exchange-traded funds (ETFs) seeking to deliver 2x and 3x daily returns of the index delivered substantially negative returns. Roughly two-thirds of the difference between the returns of the index and the levered ETFs can be attributed to compounding and volatility. The remaining difference is explained by the covariance between the ETFs' deviations from constant leverage and the index's return.

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

Prediction-market price moves are widely treated as informationally equivalent: a price jump is read the same way regardless of whether it reflects durable Bayesian updating, transient liquidity pressure, strategic position adjustment, or genuine disagreement. This paper formalizes the Signal Credibility Index (SCI) introduced in Nechepurenko (2026) as a stand-alone diagnostic. We make four contributions: (i) a revised persistence component using the persistence ratio PR(t,w) on logit prices, well-defined on short rolling windows; (ii) a weighted Cobb-Douglas form SCI(ααα) with flow-based concentration HHI_flow; (iii) a time-varying specification SCI(t; w) for real-time monitoring; and (iv) Monte Carlo validation including an out-of-distribution stress test, coordinated multi-wallet manipulation, and a logistic-regression benchmark. The validation establishes discrimination among designed microstructure regimes, not external evidence of downstream coordination effects. We document two failure modes consistent with the index targeting coordination credibility rather than pure information content: a Type II error on informed-but-concentrated whale repricing, and a Type I error on coordinated multi-wallet manipulation.

Organizations routinely make strategic budget allocations under operational constraints, but often lack a principled way to assess whether realized allocations were close to the best feasible choices in hindsight. We present a retrospective auditing framework based on hindsight regret, defined as the opportunity cost of the realized allocation relative to a constraint-faithful benchmark under the same budget and stability guardrails. The framework estimates regime-specific spend--response functions from historical logs, computes feasible hindsight allocations via constrained optimization, and propagates uncertainty through Monte Carlo evaluation to produce regret distributions, expected lift, and probability-of-improvement summaries. This separates allocation inefficiency from uncertainty in the estimated response surfaces. Experiments on real marketing allocation logs show that the framework yields interpretable post-hoc diagnostics and reveals a practical trade-off between allocation flexibility and detectability: moderate feasible reallocations often capture most measurable gain, while larger shifts move into weak-support regions with higher uncertainty. The result is a practical method for auditing historical budget decisions when online experimentation is costly or infeasible.

This paper develops a geometric diagnostic framework for classical inequality decomposability. Representing the simplest nontrivial setting of three-person income distributions as points on the two-dimensional income-share simplex, we translate population-share-weighted and income-share-weighted decomposability into concrete geometric restrictions on within- and between-group residuals, making it possible to localise and characterise violations across measures. Applied to the Mean Log Deviation, the Gini coefficient, the coefficient of variation, and the Theil index, the analysis shows that decomposability is not a binary property as measures fail in qualitatively distinct ways, and the between-group residual is consistently the primary locus of failure. Negative between-group residuals render the decomposition uninterpretable and arise for the coefficient of variation and the Theil index under population-share weighting, and for the Mean Log Deviation under income-share weighting. Stylised numerical examples quantify the resulting misinterpretation scenarios for applied researchers.

This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the traditional normal returns setting, allowing investors to capture both heavy-tailed and skewed market dynamics. We provide explicit portfolio weights for the variance and VaR approximation. Our second contribution is the numerical representation of portfolio weights, obtained from numerical optimization for better VaR approximations. The effect of skewness on the portfolio weights is quantified by comparing our optimal skew t weights with those generated in the Student t setting. We also find that, as expected, a better VaR approximation risk measure yields optimal portfolio weights which are more different than the variance optimal weights.

Digital platforms increasingly face a common challenge in the age of artificial intelligence (AI): how to elicit richer and more useful user-generated content (UGC) without fully automating content production. We study this question in the context of online reviews by examining Yelp's introduction of an AI-enabled topic nudging tool in 2023, which provides real-time prompts to guide reviewers in addressing key dimensions of the dining experience as they write. Using more than 1.5 million Yelp reviews and a differences-in-differences design, we find that AI-enabled topic nudges significantly reshape review generation. The nudges expand topical coverage, especially for underrepresented aspects such as service and ambiance, and lead to longer reviews, but they also reduce overall review volume. In addition, reviews become more textually complex and less readable, and receive fewer helpfulness votes on average. Further analysis shows that the decline in perceived helpfulness is mitigated when review content remains concentrated on a dominant dimension, highlighting the importance of informational focus. We also find heterogeneous effects: less experienced users expand topical coverage and review length more strongly, whereas experienced users exhibit greater complexity and larger declines in perceived helpfulness. Our findings extend research on AI and UGC by highlighting a distinct mode of AI deployment-guiding human contributions rather than generating content on users' behalf-and by revealing its benefits and unintended consequences for platform design.

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true risk. This paper identifies three fundamental inconsistencies: (i) volatility is path-independent and blind to temporal dependence and non-stationarity; (ii) its relevance collapses in derivative-intensive strategies, where volatility often represents opportunity rather than risk; and (iii) it lacks an absolute benchmark, providing no guidance on what level of volatility is economically ``fair'' in efficient markets. To address these limitations, we propose a new paradigm that reconceptualizes risk in terms of predictability rather than variability. Building on a general class of stochastic processes, we derive an analytical link between volatility and the Hurst-Holder exponent within the Multifractional Process with Random Exponent (MPRE) framework. This relationship yields a formal definition of ``fair volatility'', namely the volatility implied under market efficiency, where prices follow semi-martingale dynamics. Extensive empirical analysis on global equity indices supports this framework, showing that deviations from fair volatility provide a tractable measure of market inefficiency, distinguishing between momentum-driven and mean-reverting regimes. Our results advance both the theoretical foundations and empirical assessment of financial risk, offering a definition of volatility that is efficiency-consistent and economically interpretable.

The rapidly evolving cryptocurrency market presents unique challenges for investment due to its inherent volatility and evolving regulatory environment. Collective price movements can be exploited to construct diversified portfolios with improved risk-return profiles. This paper introduces an integrated framework that combines network analysis, price forecasting, and portfolio theory to identify stable groups of highly correlated cryptocurrencies for profitable portfolio construction. We employ the Louvain community detection algorithm together with consensus clustering to extract temporally persistent correlation clusters, and incorporate ARIMA-based price forecasts to enhance forward-looking cluster formation. Using 5 years of daily closing prices, we evaluate portfolio performance across multiple strategies and holding horizons, assessing both profitability and downside risk with return-based and tail-risk metrics. Our empirical results show that predictive consensus-clustering portfolios maintain consistently positive and stable performance up to a 14-day horizon, exhibit favourable gain-loss asymmetry, and achieve tighter tail-risk control. These findings demonstrate that stable interdependencies in cryptocurrency markets can be leveraged to construct profitable and risk-aware portfolios across short-term holding horizons.