arXiv subjects

Mario Wüthrich

Publications and source records attributed to Mario Wüthrich.

5 recordsLinked to original sources

arXiv2026

Measures of predictive accuracy, miscalibration and discrimination

We study the evaluation of real-valued point predictors under the decision-theoretic framework of mean-consistent loss functions given by the Bregman divergences. We first derive a new version of Murphy's decomposition of the expected loss which does not directly include the response itself but only its predictors. We then relate the miscalibration and the discrimination component of Murphy's decomposition to Lorenz-curve-based accuracy measures that are widely used in practice. Besides the usual area between the concentration and Lorenz curves, ABC, we introduce a mean-squared version ABC$^2$ that mitigates some of the weaknesses of the original ABC in identifying mean-calibration. More importantly, both ABC and ABC$^2$ are shown to rely on predictor-dependent weights, so they fail to align with the class of mean-consistent scoring functions. In the same spirit, we derive a similar result for the widely used Gini score. These results indicate that ABC, ABC$^2$ and Gini scores may lead to misleading evaluation of point predictions when used for model selection; this gives support to use mean-consistent loss functions and their Murphy's decomposition. Finally, we study forecast dominance when Lorenz curves intersect. In the one-crossing case, we establish weaker dominance criteria for subclasses of Bregman divergences through third-degree stochastic dominance.

stat.ME↗

arXiv2026

Reinforcement Learning for Micro-Level Claims Reserving

Outstanding claim liabilities are revised repeatedly as claims develop, yet most modern reserving models are trained as one-shot predictors and typically learn only from settled claims. We formulate individual claims reserving as a claim-level Markov decision process in which an agent sequentially updates outstanding claim liability (OCL) estimates over development, using continuous actions and a reward design that balances accuracy with stable reserve revisions. A key advantage of this reinforcement learning (RL) approach is that it can learn from all observed claim trajectories, including claims that remain open at valuation, thereby avoiding the reduced sample size and selection effects inherent in supervised methods trained on ultimate outcomes only. We also introduce practical components needed for actuarial use -- initialisation of new claims, temporally consistent tuning via a rolling-settlement scheme, and an importance-weighting mechanism to mitigate portfolio-level underestimation driven by the rarity of large claims. On CAS and SPLICE synthetic general insurance datasets, the proposed Soft Actor-Critic implementation delivers competitive claim-level accuracy and strong aggregate OCL performance, particularly for the immature claim segments that drive most of the liability.

q-fin.RM↗

arXiv2025

Universal Inference for Testing Calibration of Mean Estimates within the Exponential Dispersion Family

Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating mean-calibration, and we discuss the Likelihood Ratio Test (LRT) within the Exponential Dispersion Family (EDF). Then, we investigate the framework of universal inference to test for mean-calibration. We develop a sub-sampled split LRT within the EDF that provides finite sample guarantees with universally valid critical values. We investigate type I error, power and e-power of this sub-sampled split LRT, we compare it to the classical LRT, and we propose a novel test statistics based on the sub-sampled split LRT to enhance the performance of the calibration test. A numerical analysis verifies that our proposal is an attractive alternative to the classical LRT achieving a high power in detecting miscalibration.

stat.AP↗

arXiv2023

Smoothness and monotonicity constraints for neural networks using ICEnet

Deep neural networks have become an important tool for use in actuarial tasks, due to the significant gains in accuracy provided by these techniques compared to traditional methods, but also due to the close connection of these models to the Generalized Linear Models (GLMs) currently used in industry. Whereas constraining GLM parameters relating to insurance risk factors to be smooth or exhibit monotonicity is trivial, methods to incorporate such constraints into deep neural networks have not yet been developed. This is a barrier for the adoption of neural networks in insurance practice since actuaries often impose these constraints for commercial or statistical reasons. In this work, we present a novel method for enforcing constraints within deep neural network models, and we show how these models can be trained. Moreover, we provide example applications using real-world datasets. We call our proposed method ICEnet to emphasize the close link of our proposal to the individual conditional expectation (ICE) model interpretability technique.

cs.LG↗

arXiv2016

Consistent Recalibration of Yield Curve Models

The analytical tractability of affine (short rate) models, such as the Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the dynamics of real data, these models need to exhibit time-dependent or even stochastic parameters. This in turn breaks their tractability, and modelling and simulating becomes an arduous task. We introduce a new class of Heath-Jarrow-Morton (HJM) models that both fit the dynamics of real market data and remain tractable. We call these models consistent recalibration (CRC) models. These CRC models appear as limits of concatenations of forward rate increments, each belonging to a Hull-White extended affine factor model with possibly different parameters. That is, we construct HJM models from "tangent" affine models. We develop a theory for a continuous path version of such models and discuss their numerical implementations within the Vasicek and Cox-Ingersoll-Ross frameworks.

q-fin.MF↗