Risk management is an important part of financial practice, essential for protecting assets and investments in modern-day volatile markets. This paper proposes a mixture of mirrored Weibull (MMW) distribution for modelling stock returns and estimating risk measures. Unlike common practices which are typically based on the normal distribution, the MMW model can flexibly accommodate non-normal features frequently exhibited in financial data. It also enjoys appealing properties such as having a simple density expression and fast parameter estimation. We demonstrate the effectiveness of our model by assessing its performance in Value-at-Risk (VaR) estimation of three S&P500 stocks. The MMW model compares favourably to Gaussian mixture model and t-mixture model, with significant improvements in VaR estimation and prediction.

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical. The model captures realistic features observed in many economic observables, which can be explained as market-driven firm entries/exits, worker inflow/outflow, and income growth/loss. This model is not conservative and, despite the asymmetry in the entry and exit rates, we find that the system eventually relaxes to a stationary distribution. Moreover, our analysis reveals three distinct dynamical regimes in the moments of the distribution, arising from the interplay between volatility, drift, entry, and exit rates. We further derive the survival probability and the mean first-passage time associated with the observed variable reaching certain threshold under the competing entry-exit processes. Interestingly, we identify an optimal exit rate that minimizes the mean first-passage time, providing insights into how entry and exit policies can influence the outcome of the system. These results should be useful for understanding the long-run behavior of economic systems in which growth, volatility, entry, and exit jointly shape the evolution of heterogeneous units.

Many policy counterfactuals depend on how consumers value product attributes such as sugar, sodium, caffeine, alcohol, or emissions. Standard hedonic and differentiated-products models interpret these valuations statically. That interpretation is restrictive when attributes are habit forming: observed prices then reflect both contemporaneous marginal value and the continuation value generated by current consumption. I develop a nonparametric revealed-preference framework for dynamic hedonic valuation, deriving necessary and sufficient conditions for rationalising observed prices and choices. Using household scanner data on cereal purchases, I show that the hedonic representation places real restrictions on prices, while habit formation improves behavioural coherence conditional on that representation. The results provide a diagnostic for when static attribute valuation is justified and when prices reveal more than contemporaneous marginal values.

We study the problem of forecasting and optimally trading day-ahead versus real-time (DART) price spreads in U.S. wholesale electricity markets. Building on the framework of Galarneau-Vincent et al., we extend spike prediction from a single zone to a multi-zone setting and treat both positive and negative DART spikes within a unified statistical model. To translate directional signals into economically meaningful positions, we develop a structural and market-consistent price impact model based on day-ahead bid stacks. This yields closed-form expressions for the optimal vector of zonal INC/DEC quantities, capturing asymmetric buy/sell impacts and cross-zone congestion effects. When applied to NYISO, the resulting impact-aware strategy significantly improves the risk-return profile relative to unit-size trading and highlights substantial heterogeneity across markets and seasons.

Two MEV builders now produce nearly 80\% of Ethereum blocks. Block builders have the ability to reorder transactions on the blockchain in a way that can be harmful to participants. We estimate they would pay in the aggregate nearly \$14 million per month to ensure that they remained in the first quartile of the block. Sandwich attacks, in which a transaction is front-run, are frequent, averaging more than one per block. Gas fees on these transactions pay for nearly 15\% of the MEV payments to the validator. These attacks have especially large marginal effects and skew the distribution. Reforms such as gas fee priority or private transaction pools might be helpful.

We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement to an entire set of positions. We develop an axiomatic framework for SRMs, adapting classical properties such as monotonicity, translation invariance, convexity, and positive homogeneity to set arithmetic. The main technical contribution is a dual representation of convex SRMs through the \strict{} topology and regular $τ$-additive unit-mass measures. We also characterize worst-case SRMs and present examples related to systemic risk, Knightian uncertainty, and preference representations.

This study investigates the macroeconomic determinants and dynamic behaviour of personal remittances as a share of Gross Domestic Product (GDP) in Nepal, emphasizing external demand in major destination countries and domestic monetary policy. Using annual data (1993-2024), we construct composite indices via Principal Component Analysis (PCA) for multi-country external demand and a domestic Monetary Conditions Index (MCI). Our small-sample econometric pipeline includes Autoregressive Distributed Lag (ARDL) bounds testing, Engle-Granger cointegration, Dynamic OLS (DOLS), and a two-step Error Correction Model (ECM). We also employ Granger causality tests and multi-model forecasting using machine learning and ECM scenarios. The analysis reveals a strong positive long-run effect of external demand on remittances and a significant negative impact of tighter domestic monetary conditions. The ECM confirms a stable cointegrating relationship, correcting approximately 26% of disequilibria annually. Medium-term projections indicate remittances will remain structurally important, reaching around 28.3% of GDP by 2030 under baseline conditions, while exhibiting high sensitivity to external demand shocks. This study advances the literature by integrating PCA-derived external demand and monetary conditions indices within a unified ARDL-ECM framework for small samples. Focusing on one of the world's most remittance-dependent economies, it offers actionable insights for monetary policy calibration, migration diversification, and the productive utilization of remittance inflows.

This chapter reviews indirect estimators of intergenerational mobility, focusing on approaches that infer parent-child or other family associations when direct income data are incomplete or unavailable. We synthesize methods based on instrumental variables, imputation using observable characteristics such as education and occupation, surname-based estimators, and multigenerational linkages. To unify these approaches, we introduce a stylized framework in which socioeconomic status is transmitted through multiple pathways with heterogeneous persistence rates. Within this framework, both direct and indirect estimators can be interpreted as weighted averages of these underlying transmission channels. A central insight is that the choice of instrument or imputation strategy determines these weights, leading different methods to capture distinct aspects of the transmission process. We highlight implications for interpretation, showing that indirect estimators need not recover conventional parent-child correlations but can instead provide complementary evidence on long-run persistence and the mechanisms underlying persistent inequalities.

Financial options are fundamental to traditional markets, enabling strategies ranging from hedging to speculating. Yet, while the Automated Market Maker paradigm has revolutionized decentralized spot markets, no equivalent standard has emerged for on-chain options. Typical designs attempt to replicate centralized exchange mechanics, requiring high-frequency oracles and robust liquidation engines which may fail during stress events. This paper presents a design for amortizing perpetual options tailored to the operational and adversarial constraints of blockchain environments. Leveraging this primitive, we introduce a decentralized market framework with minimal consistency requirements. We demonstrate that this contract functions as a foundational risk primitive for DeFi, enabling applications such as endogenous collateralization and explicitly priced de-peg insurance, thereby showing that this design provides a layer for mutualizing tail risk across protocols without reliance on centralized clearing institutions.

We provide here a universal approximation theorem with precise quantitative error bounds for noisy quantum neural networks. We focus on applications to Quantitative Finance, where target functions are often given as expectations. We further provide a detailed numerical analysis, testing our results on actual noisy quantum hardware.

The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body problem. By adopting a mean-field approach, this many-body problem can be approximated by a non-linear one-body problem, which in turn leads to a transparent pricing method for disability coverages based on a lower-dimensional system of non-linear forward integro-differential equations. In a practice-oriented simulation study, the mean-field approximation clearly stands its ground in comparison to naïve Monte Carlo methods.

The automated mining of predictive signals, or alphas, is a central challenge in quantitative finance. While Reinforcement Learning (RL) has emerged as a promising paradigm for generating formulaic alphas, existing frameworks are fundamentally hampered by a triad of interconnected issues. First, they suffer from reward sparsity, where meaningful feedback is only available upon the completion of a full formula, leading to inefficient and unstable exploration. Second, they rely on semantically inadequate sequential representations of mathematical expressions, failing to capture the structure that determine an alpha's behavior. Third, the standard RL objective of maximizing expected returns inherently drives policies towards a single optimal mode, directly contradicting the practical need for a diverse portfolio of non-correlated alphas. To overcome these challenges, we introduce AlphaSAGE (Structure-Aware Alpha Mining via Generative Flow Networks for Robust Exploration), a novel framework is built upon three cornerstone innovations: (1) a structure-aware encoder based on Relational Graph Convolutional Network (RGCN); (2) a new framework with Generative Flow Networks (GFlowNets); and (3) a dense, multi-faceted reward structure. Empirical results demonstrate that AlphaSAGE outperforms existing baselines in mining a more diverse, novel, and highly predictive portfolio of alphas, thereby proposing a new paradigm for automated alpha mining. Our code is available at https://github.com/BerkinChen/AlphaSAGE.

Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the naïve estimate of the winner is upward biased. We distinguish two forms of winner's curse, bias relative to the true best treatment (global) and bias relative to the selected treatment's true mean (selective), and link them to regret from deploying a suboptimal treatment. This framework defines seven decision-relevant evaluation targets: mean bias, mean squared error, and confidence interval coverage for the global and selective winner's curse, and mean regret. We then show that methods that perform well on one target can perform poorly on others, so corrections should be matched to the manager's objective. Across simulations with varying effect sizes, multiple-arm settings, and data calibrated to an online A/B testing platform, no method dominates uniformly: the plug-in estimator performs best when treatment differences are large, cross-fitting performs best when treatments are similar, and resampling methods often achieve low mean squared error for moderate differences. We also introduce an adaptive empirical likelihood procedure that delivers asymptotically valid confidence intervals across settings without the tuning sensitivity of resampling-based methods.

The rapid diffusion of agentic AI has created a new coverage problem for commercial insurance: some AI-mediated losses are now affirmatively insured, some create silent-AI exposure under legacy cyber, technology errors-and-omissions (E&O), directors-and-officers (D&O), employment practices liability (EPLI), crime, and media policies, and others are being actively excluded. This paper maps that emerging boundary by coding 55 AI threat classes against 26 insurance products, endorsements, and exclusion regimes using public carrier materials and OWASP/MITRE threat catalogs. We identify a four-tier insurability frontier: affirmatively insured perils, silent-AI exposures, actively excluded perils, and perils outside conventional private insurance structures. Our coding measures publicly claimed positioning rather than executed contract wording; the headline statistics describe what carriers publicly state about coverage, not what would be paid in any specific claim. Three patterns emerge. First, affirmative AI coverage is beginning to differentiate by primary risk emphasis: public materials often position Munich Re around model performance and drift, Armilla and parts of the Lloyd's market around hallucination and broader AI liability, Tokio Marine Kiln and CFC around IP and technology E&O concerns, Apollo ibott around emerging autonomous system liability, and Coalition around deepfake and AI-enabled cyber response. Second, legacy lines retain silent-AI exposure where AI is an instrumentality rather than the legal cause of loss. Third, foundation model concentration is the clearest genuinely novel insurability frontier because upstream model failure can correlate losses across many cedents at once; the relevant market design question is which insurability constraint each candidate structure relaxes, not merely which systemic risk template exists.

Scientific inference is often undermined by the vast but rarely explored "multiverse" of defensible modelling choices, which can generate results as variable as the phenomena under study. We introduce RobustiPy, an open-source Python library that systematizes multiverse analysis and model-uncertainty quantification at scale. RobustiPy unifies bootstrap-based inference, combinatorial specification search, model selection and averaging, joint-inference routines, and explainable AI methods within a modular, reproducible framework. Beyond exhaustive specification curves, it supports rigorous out-of-sample validation and quantifies the marginal contribution of each covariate. We demonstrate its utility across five simulation designs and ten empirical case studies spanning economics, sociology, psychology, and medicine, including a re-analysis of widely cited findings with documented discrepancies. Benchmarking on ~672 million simulated regressions shows that RobustiPy delivers state-of-the-art computational efficiency while expanding transparency in empirical research. By standardizing and accelerating robustness analysis, RobustiPy transforms how researchers interrogate sensitivity across the analytical multiverse, offering a practical foundation for more reproducible and interpretable computational science.