arXiv subjects

Paul Schneider

Publications and source records attributed to Paul Schneider.

14 recordsLinked to original sources

arXiv2026

Fundamental Properties of Linear Factor Models

We characterize the loading matrices that admit a conditional linear factor representation for excess returns in which the factors are traded, residual risk is unpriced, and the loadings are the betas of the factors. The characterization is a joint restriction on the loadings, the risk premia, and the second moment matrix of returns. It requires no rank assumptions, and exactly one traded factor representation attains it for given loadings: the moment-weighted factor portfolios. On Fama--French panels, characteristic loadings differ from the regression loadings of their factors by 19 to 48 percent of their size, at every estimation window.

q-fin.ST↗

arXiv2026

CrossFeat: Bridging Imaging Modalities in Feature Descriptor Space

Most advances in keypoint descriptions address monomodal settings, where image variations arise from viewpoint, illumination, or contrast changes. Multimodal scenarios involve images produced by fundamentally different sensing processes, such as multispectral imaging, RGB-depth, satellite imagery, or medical imaging, causing the same structures to appear differently. A common solution to cross-modal description is to train descriptors for each modality pair, which requires retraining whenever the modalities change, or to train large models, which incur a significant increase in runtime. Instead, we propose CrossFeat, a framework that enables an existing monomodal descriptor to operate across modalities. Our method learns a crossing function in descriptor space that maps features from one modality to a representation compatible with another. To preserve the structural information captured by the original descriptor, CrossFeat introduces a geometry-appearance disentanglement such that only appearance is altered while the geometric properties are preserved. Experiments across multiple domains and datasets demonstrate improved performance in multimodal matching.

cs.CV↗

arXiv2026

Low-rank kernel methods for American option pricing

We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation values as a learning problem in a reproducing kernel Hilbert space, in which the conditional expectation is represented as a linear operator acting on future payoffs. This perspective yields an offline-online decomposition: the operator is learned once from simulated data and subsequently reused across all exercise dates, eliminating the need to recompute regression models at each step of the backward recursion. We establish convergence guarantees and derive bounds quantifying the approximation errors across exercise dates. Numerical experiments demonstrate the speed and accuracy of the proposed approach relative to extant methods.

math.NA↗

arXiv2026

Kernel Density Machines

We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids the structural requirements common in classical nonparametric density estimators. We construct a sample estimator and prove its consistency and a functional central limit theorem. To enable scalability, we develop Nystrom-type low-rank approximations and derive optimal error rates, filling a gap in the literature where such guarantees for density learning have been missing. We demonstrate the versatility of KDM through applications to kernel-based two-sample testing and conditional distribution estimation, the latter enjoying dimension-free guarantees beyond those of locally smoothed methods. Experiments on simulated and real data show that KDM is accurate, scalable, and competitive across a range of tasks.

stat.ML↗

arXiv2026

Quantile-Based Skewness for Fuzzy Numbers with Probabilistic Foundations: With an Application in Portfolio Optimization

This paper introduces a novel parameter free skewness coefficient for fuzzy numbers, addressing a critical gap in quantifying asymmetry under imprecision. Existing fuzzy literature substitutes membership functions for probability density functions in moment-based skewness, lacking rigorous theoretical grounding. Our coefficient, however, rigorously establishes a probabilistic foundation, making it both probabilistically meaningful and fully compliant with the semantics of fuzzy set theory. Our approach interprets a fuzzy number's left and right membership function components as cumulative and survival probability functions of associated random variables. This provides a robust probabilistic foundation for its $α$-cuts as generalized quantiles representing values that are "at least $α$-probable", thereby instantiating the well-grounded dualism between probability and possibility theory. As a quantile-based measure, the proposed coefficient offers invariance under scale and location transformations. Crucially, its superior computational efficiency, empirically demonstrating an almost logarithmic reduction in portfolio optimization processing time with increasing assets, enables significant scalability for real-world applications. The coefficient comprises two complementary constituents: an "inner" measure quantifying the intrinsic skewness of the underlying probabilistic distributions, and an "outer" measure capturing the fuzzy number's overall profile asymmetry. This dual structure offers nuanced insights into a fuzzy number's asymmetry. We demonstrate its practical utility and computational advantages within a fuzzy mean-variance-skewness portfolio optimization framework, comparing its performance with two of the most highly cited original moment-based fuzzy skewness coefficients from the literature.

math.GM↗

arXiv2025

The Wisdom of Deliberating AI Crowds: Does Deliberation Improve LLM-Based Forecasting?

Structured deliberation has been found to improve the performance of human forecasters. This study investigates whether a similar intervention, i.e. allowing LLMs to review each other's forecasts before updating, can improve accuracy in large language models (GPT-5, Claude Sonnet 4.5, Gemini Pro 2.5). Using 202 resolved binary questions from the Metaculus Q2 2025 AI Forecasting Tournament, accuracy was assessed across four scenarios: (1) diverse models with distributed information, (2) diverse models with shared information, (3) homogeneous models with distributed information, and (4) homogeneous models with shared information. Results show that the intervention significantly improves accuracy in scenario (2), reducing Log Loss by 0.020 or about 4 percent in relative terms (p = 0.017). However, when homogeneous groups (three instances of the same model) engaged in the same process, no benefit was observed. Unexpectedly, providing LLMs with additional contextual information did not improve forecast accuracy, limiting our ability to study information pooling as a mechanism. Our findings suggest that deliberation may be a viable strategy for improving LLM forecasting.

cs.AI↗

arXiv2025

Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels

We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance.

stat.ME↗

arXiv2024

Fast Empirical Scenarios

We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal selects important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute and lend themselves to consistent scenario-based modeling and multi-dimensional numerical integration that can be used for interpretable decision-making under uncertainty. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed algorithms.

stat.ML↗

arXiv2024

Adaptive joint distribution learning

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym derivative, which we estimate from sample sizes of up to several millions, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. Our proposal is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.

stat.ML↗

arXiv2023

Constrained Polynomial Likelihood

We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for additional shape restrictions, as we illustrate with two empirical applications. The first develops a PLR for the unknown transition density of a jump-diffusion process, while the second extracts a positive density directly from option prices. In both cases, we show the importance of implementing the non-negativity restriction.

math.OC↗

arXiv2022

Optimal Investment and Equilibrium Pricing under Ambiguity

We consider portfolio selection under nonparametric $α$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are nondifferentiable, resemble observed bid-ask spreads, and are consistent with existing parametric limiting participation results under ambiguity. Ambiguity seekers exhibit a discontinuous demand function, implying an empty set of reservation prices. If agents have identical, or sufficiently similar prior beliefs, the first-best equilibrium is no trade. Simple conditions yield the existence of a Pareto-efficient second-best equilibrium, implying that heterogeneity in ambiguity preferences is sufficient for mutually beneficial transactions among all else homogeneous traders. These equilibria reconcile many observed phenomena in liquid high-information financial markets, such as liquidity dry-ups, portfolio inertia, and negative risk premia.

econ.GN↗

arXiv2011

Density Approximations for Multivariate Affine Jump-Diffusion Processes

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in credit risk, likelihood inference, and option pricing highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

math.ST↗

arXiv2010

Globally optimal parameter estimates for nonlinear diffusions

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of nonlinear SDEs with constant volatility and drift that is linear in the model parameters. In this setting, globally optimal parameters are obtained in a single step by solving a linear system. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.

math.ST↗

arXiv2009

Empirical asset pricing with nonlinear risk premia

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physical measure, thus allowing to work with nonlinear models for the real world dynamics not considered in the literature so far. It emerges that the additional flexibility in the time series modelling is econometrically relevant: a nonlinear stochastic volatility diffusion model for the joint time series of the S&P 100 and the VXO implied volatility index data shows superior forecasting power over the standard specifications for implied and realized variance forecasting.

q-fin.ST↗