Probability and Risk Models

Latest papers

• A Practical Guide on Graphical Model Validation

  Mario V. W\"uthrich · 23 September 2026

  This manuscript formalizes the most popular model validation tools used in general insurance actuarial modeling. These include graphical tools like calibration plots, actual-vs-expected plots, lift charts, Murphy diagrams, as well as classical statistical tools such as Bregman losses, deviance losse…

• Scaling Laws, Tabular Data and Actuarial Ratemaking Models

  Ronald Richman · 4 September 2026

  Scaling laws in modern deep learning describe how held-out loss improves as model capacity, training data, and compute increase, often following power-law trends. We investigate whether analogous scaling regularities arise in actuarial ratemaking, where data are tabular, heterogeneous, and noisy, an…

• Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning

  Lars van der Laan, Nathan Kallus · 26 August 2026

  Marginalized importance weighting evaluates a target policy by reweighting offline state-action samples with its discounted occupancy ratio, characterized by an adjoint Bellman equation. Existing minimax, primal-dual, and fitted fixed-point estimators can leave residual occupancy-balance violations …

• Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance

  Mark\'eta Kr\'upov\'a (CEREMADE), Nabil Rachdi (CEREMADE), Quentin Guibert (CEREMADE) · 23 June 2026

  With the rapid development of machine learning and deep learning techniques, actuaries and the broader insurance industry face a persistent trade-off between predictive accuracy and interpretability. This paper provides a comprehensive applied assessment of Explainable Boosting Machines (EBM) in a c…

• On Local Population-Risk Certificates

  Mingzhi Song · 18 June 2026

  This paper develops local certificates for population-risk increments around a current model. For a local candidate set \(\mathcal D\), the certificate is a two-sided confidence band for \(P({\ell_{\theta+v}-\ell_\theta})\) over \(v\in\mathcal D\). As an application, the upper endpoint of this band …

• Gradient boosting for extremes: sampling theory and application to insurance

  St\'ephane Lhaut, Olivier Lopez · 15 June 2026

  We develop a statistical learning theory for gradient boosting applied to the estimation of covariate-dependent Generalized Pareto (GP) distributions in the context of Peaks-over-Threshold modeling. After an orthogonal reparametrization of the GP likelihood that diagonalizes its Fisher information m…

• Statistical Decision Theory with Counterfactual Loss

  Benedikt Koch, Kosuke Imai · 9 June 2026

  Many researchers apply classical statistical decision theory to evaluate treatment choices and learn optimal policies. However, because this framework relies solely on realized outcomes under chosen actions and ignores counterfactuals, it cannot assess the quality of a decision relative to feasible …

• Is TabPFN the Silver Bullet for Insurance Pricing?

  Bruno Deprez, Wouter Verbeke, Tim Verdonck · 25 May 2026

  Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models, with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) offer a fundamentally different paradigm. By pre-training on large col…

• A Hybrid Framework for Reinsurance Optimization: Integrating Generative Models and Reinforcement Learning

  Stella C. Dong · 24 March 2026

  Reinsurance optimization is a cornerstone of solvency and capital management, yet traditional approaches often rely on restrictive distributional assumptions and static program designs. We propose a hybrid framework that combines Variational Autoencoders (VAEs) to learn joint distributions of multi-…

• Global Minimizers of Sigmoid Contrastive Loss

  Kiril Bangachev, Guy Bresler, Iliyas Noman, Yury Polyanskiy · 12 March 2026

  The meta-task of obtaining and aligning representations through contrastive pretraining is steadily gaining importance since its introduction in CLIP and ALIGN. In this paper we theoretically explain the advantages of synchronizing with trainable inverse temperature and bias under the sigmoid loss, …

• Synthetic data for ratemaking: imputation-based methods vs adversarial networks and autoencoders

  Yevhen Havrylenko, Meelis K\"a\"arik, Artur Tuttar · 10 March 2026

  Actuarial ratemaking depends on high-quality data, yet access to such data is often limited by the cost of obtaining new data, privacy concerns, etc. In this paper, we explore synthetic-data generation as a potential solution to these issues. In addition to generative methods previously studied in t…

• Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach

  Zhengyi Guo, Wenpin Tang, Renyuan Xu · 6 February 2026

  We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event simulation, where soft or reward-based guidance methods offer no…

• A new strategy for finite-sample valid prediction of future insurance claims in the regression setting

  Liang Hong · 30 January 2026

  The extant insurance literature demonstrates a paucity of finite-sample valid prediction intervals of future insurance claims in the regression setting. To address this challenge, this article proposes a new strategy that converts a predictive method in the unsupervised iid (independent identically …

• Reinforcement Learning for Micro-Level Claims Reserving

  Benjamin Avanzi, Ronald Richman, Bernard Wong, Mario W\"uthrich, Yagebu Xie · 13 January 2026

  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 u…

• On the use of case estimate and transactional payment data in neural networks for individual loss reserving

  Benjamin Avanzi, Matthew Lambrianidis, Greg Taylor, Bernard Wong · 12 January 2026

  The use of neural networks trained on individual claims data has become increasingly popular in the actuarial reserving literature. We consider how to best input historical payment data in neural network models. Additionally, case estimates are also available in the format of a time series, and we e…

• Fundamental limits for weighted empirical approximations of tilted distributions

  Sarvesh Ravichandran Iyer, Himadri Mandal, Dhruman Gupta, Rushil Gupta, Agniv Bandhyopadhyay, Achal Bassamboo, Varun Gupta, Sandeep Juneja · 1 January 2026

  Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asym…

• Stochastic Optimization with Optimal Importance Sampling

  Liviu Aolaritei, Bart P. G. Van Parys, Henry Lam, Michael I. Jordan · 23 December 2025

  Importance Sampling (IS) is a widely used variance reduction technique for enhancing the efficiency of Monte Carlo methods, particularly in rare-event simulation and related applications. Despite its effectiveness, the performance of IS is highly sensitive to the choice of the proposal distribution …

• Towards Data Valuation via Asymmetric Data Shapley

  Xi Zheng, Xiangyu Chang, Ruoxi Jia, Yong Tan · 20 November 2025

  As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory, has been widely adopted to assess the contribution of individu…

• Doubly-Robust Estimation of Counterfactual Policy Mean Embeddings

  Houssam Zenati, Bariscan Bozkurt, Arthur Gretton · 29 October 2025

  Estimating the distribution of outcomes under counterfactual policies is critical for decision-making in domains such as recommendation, advertising, and healthcare. We propose and analyze a novel framework-Counterfactual Policy Mean Embedding (CPME)-that represents the entire counterfactual outcome…