There has long been an apparent consensus in the literature on intra-household allocation and fertility that greater paternal involvement in childcare relaxes maternal time constraints, enabling mothers to increase their labor supply or leisure. Recent evidence, particularly from South Korea, challenges this view: increases in fathers' childcare time have coincided with a further increase in mothers' time dedicated to child-rearing. This paper develops an Overlapping Generations (OLG) growth model to address such a puzzle. The central mechanism and our main innovation hinge on the functional form of the childcare technology. When maternal and paternal time are substitutes, the conventional result holds. However, when they are complements, greater paternal involvement necessarily raises maternal childcare time, depressing fertility and redirecting household resources toward child quality. We further argue that the elasticity of substitution should not be interpreted as a pure preference parameter, as it also reflects the social and institutional norms, the skills each parent brings to child-rearing and their intergenerational transmission. The model is extended to study the effectiveness of pro-natalist subsidies, suggesting that such policies may generate an unintended anti-fertility bias. Numerical simulations calibrated loosely to South Korean data confirm that the model is consistent with the observed quantity-quality trade-off and the persistence of low fertility despite active pro-natalist policy.

Predicting cross-sectional stock returns is challenging due to low signal-to-noise ratios and evolving market regimes. Classical factor models offer interpretability but limited flexibility, while deep learning models achieve strong performance yet often underutilize financial priors. We address this gap with PRISM-VQ (PRior-Informed Stock Model with Vector Quantization), a dynamic factor framework that integrates expert prior factors, vector-quantized discrete latent factors learned from cross-sectional structure, and a structure-conditioned Mixture-of-Experts to generate time-varying factor loadings. Vector quantization acts as an information bottleneck that suppresses noise while capturing robust market structure, with discrete codes serving both as latent factors and as routing signals for temporal expert specialization. Experiments on CSI 300 and S&P 500 show consistent improvements in cross-sectional return prediction and portfolio performance over strong baselines while preserving interpretability. Our code is available at https://github.com/finxlab/PRISM-VQ.

Given the challenge of achieving societal welfare in an environmentally sustainable way, the Index of Sustainable Economic Welfare (ISEW) has emerged as an alternative indicator of progress in response to critiques of Gross Domestic Product (GDP). The ISEW compares the benefits of economic activity with its social and environmental costs. So far, most studies empirically analyse the ISEW for past developments, while no studies have simulated the ISEW using a dynamic macroeconomic model. We address this important gap by incorporating the ISEW into COMPASS, an ecological macroeconomic model that features the Doughnut of biophysical boundaries and social thresholds. First, we analyse how the ISEW is affected by three social and environmental policies: a carbon tax, income redistribution, and working-time reduction. We find that the ISEW grows in all scenarios. The strongest improvement over business-as-usual arises when all policies are combined, while the individual policies mostly affect the ISEW positively. Only in the case of working-time reduction, the ISEW decreases. Our study underscores the benefit of dynamically modelling the ISEW for anticipating the net effect of multiple impulses and their interconnections on the indicator. Second, we explore how the ISEW compares to GDP and the Doughnut when evaluating social and environmental policies. Our results suggest that the ISEW is better than GDP at capturing their effects, but it omits the full environmental costs of growth. We argue that the Doughnut, with its comprehensive picture of biophysical boundaries and social thresholds, provides better guidance for policymakers striving for sustainable wellbeing.

We conduct the first rigorous study of electricity price volatility for the full panel of electricity prices across three European generation zones. By interpreting the observed day-ahead prices as local averages of a latent price process governed by a stochastic partial differential equation, we develop estimators of the weekly integrated variance. The inherently infinite dimensional setting introduce several complications that are not relevant in the conventional finite dimensional semimartingale setting, and we spend considerable effort in dealing with these. In particular, we must account for both mean-reversion in prices and semigroup-smoothing in the estimated variance. We provide a detailed decomposition and interpretation of the empirical estimates across three vastly different European generation zones, namely Germany, Norway, and Spain. Our findings indicate that each zone has very different drivers of volatility, and that the impact of generation variables differs considerably. We document that leverage effects appear to be present at first sight, but disappear once we condition on suitable state variables, thereby showing that electricity price volatility does not generally exhibit asymmetric responses to price shocks.

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

This paper studies when strategic understanding acquired in one mechanism can be transferred to another. We introduce a framework in which agents' knowledge is represented as a set of payoff comparisons they can make, and use it to formalize what it means to understand that a strategy profile is an equilibrium. We first apply this framework to mechanisms that are strategically equivalent-that is, share the same game form up to relabeling of actions-and show that agents' understanding of equilibrium transfers across such mechanisms once the relevant action correspondences are explained to them. We then define strategic analogy, a weaker notion that allows not only actions but also types to be remapped, and show that understanding of equilibrium transfers across strategically analogous mechanisms once agents recognize how actions and types correspond. Applications include single-item auctions, scoring auctions, and nonlinear pricing with capacity constraints.

We study ballot exhaustion in multiwinner single transferable vote (STV) elections using a dataset of 1,070 Scottish local government elections comprising over 5.4 million ballots. While ballot exhaustion has been studied extensively in single-winner elections, comparatively little work examines exhaustion in the multiwinner setting. We introduce formal definitions of several types of exhaustion in STV elections, distinguishing between exhausted ballots, non-first-choice exhausted ballots, unrepresented exhausted ballots, and weight exhaustion. These definitions clarify important conceptual differences between ballots that cease to transfer and ballots that fail to contribute meaningfully to representation. Our empirical analysis shows that 27.9\% of ballots are exhausted by the final round of counting, although the corresponding weight exhaustion rate is only 7.1\%, indicating that many exhausted ballots have already contributed to the election of a candidate. Moreover, most exhausted ballots correspond to voters who achieve some form of representation, either because their first-ranked candidate wins or because a candidate ranked among their top choices is elected. These results suggest that raw exhaustion rates alone substantially overstate the extent to which voters lose their influence or fail to obtain representation under STV. We also investigate whether exhaustion can affect electoral outcomes by extending partial ballots under several completion models. Under extreme assumptions, exhaustion can potentially alter a substantial number of outcomes, but under a proportional ballot-completion model only 3.5\% of seats change. Finally, we show that a substantial number of winners fail to reach quota, even after the elimination of all losing candidates. These results help clarify the practical and normative significance of ballot exhaustion in real-world STV elections.

We investigate the martingale Schrödinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to arbitrary dimension and admits several equivalent characterizations. In particular, we identify its continuous-time counterpart as the continuous martingale with prescribed marginals that minimizes a weighted quadratic energy measuring the deviation from Brownian motion. In the irreducible case, we prove that this continuous martingale Schrödinger bridge coincides with the Föllmer martingale, that is, with the Doob martingale associated to a suitable Föllmer process. More generally, we relate the martingale Schrödinger bridge to a variational problem over base measures and to the dual formulation of the corresponding weak optimal transport problem, thereby clarifying its connection with the classical Schrödinger bridge.

I propose a functional on the space of spectral risk measures that quantifies their ``degree of risk aversion''. This quantification formalizes the idea that some risk measures are ``more risk-averse'' than others. I construct the functional using two axioms: a normalization on the space of CVaRs and a linearity axiom. I present two formulas for the functional and discuss several properties and interpretations.

This paper considers finitely many investors who perform mean-variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of all investors. At the inter-personal level, each investor selects a trading strategy in response to others' strategies. This selected strategy additionally needs to yield an equilibrium intra-personally, so as to resolve time inconsistency among the investor's current and future selves (triggered by the mean-variance objective). A Nash equilibrium we look for is thus a tuple of trading strategies under which every investor achieves her intra-personal equilibrium simultaneously. We derive such a Nash equilibrium explicitly in the idealized case of full information (i.e., the dynamics of the underlying stock is perfectly known) and semi-explicitly in the realistic case of partial information (i.e., the stock evolution is observed, but the expected return of the stock is not precisely known). The formula under partial information consists of the myopic trading and intertemporal hedging terms, both of which depend on an additional state process that serves to filter the true expected return and whose influence on trading is captured by a degenerate Cauchy problem. Our results identify that relative performance criteria can induce downward self-reinforcement of investors' wealth--if every investor suffers a wealth decline simultaneously, then everyone's wealth tends to decline further. This phenomenon, as numerical examples show, is negligible under full information but pronounced under partial information.

We apply the procedure of Lee et al. to the problem of performing inference on the signal-noise ratio of the asset which displays maximum sample Sharpe ratio over a set of possibly correlated assets. We find a multivariate analogue of the commonly used approximate standard error of the Sharpe ratio to use in this conditional estimation procedure. We also consider several alternative procedures, including the simple Bonferroni correction for multiple hypothesis testing, which we fix for the case of positive common correlation among assets, the chi-bar square test against one-sided alternatives, Follman's test, and Hansen's asymptotic adjustments. Testing indicates the conditional inference procedure achieves nominal type I rate, and does not appear to suffer from non-normality of returns. The conditional estimation test has low power under the alternative where there is little spread in the signal-noise ratios of the assets, and high power under the alternative where a single asset has high signal-noise ratio. Unlike the alternative procedures, it appears to enjoy rejection probabilities monotonic in the signal-noise ratio of the selected asset, and actually maintains near-nominal rejection rates under the conditional null.

Conventional algorithmic trading systems are grounded in deterministic heuristics or offline-trained statistical models that cannot adapt to the semantic complexity of rapidly shifting market regimes. This paper introduces AGENTICAITA, an agentic AI framework that replaces the traditional signal then execute paradigm with a fully autonomous deliberative loop in which multiple specialized Large Language Model agents reason, negotiate, and act in concert - without any offline training or human intervention. The framework proposes four architectural contributions: (i) an Adaptive Z-Score Trigger Engine that acts as a cognitive resource allocator, gating LLM inference exclusively on statistically anomalous market conditions; (ii) a Sequential Deliberative Pipeline - the core agentic contribution - in which an Analyst agent, a Risk Manager agent, and an Executor agent form a structured reasoning chain governed by typed JSON contracts and a deterministic hard-gate safety layer; (iii) an Inference Gating Protocol, a mutex-based cognitive resource scheduler that serializes concurrent agent activations and ensures fully reproducible audit trails; and (iv) a Correlation-Break Diversification composite score that operationalizes portfolio-level idiosyncratic signal prioritization within individual agent reasoning. Validated over a five-day autonomous dry-run session under live market conditions, the framework demonstrates operational correctness of the deliberative pipeline, achieving 157 zero-intervention invocations across 76 assets with an 11.5% agentic friction rate that confirms non-trivial inter-agent negotiation. This preliminary proof-of-concept establishes the feasibility of training-free, deterministic safety-constrained multi-agent orchestration in financial decision loops, with statistically robust performance evaluation and execution cost modeling deferred to extended live deployment.