用于评估财产保险中住宅洪水风险的贝叶斯空间建模框架
Bayesian spatial modelling framework for assessing residential flood risk in property insurance
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中文总结 AI 辅助
研究针对保险风险建模空间异质性问题引入点参考贝叶斯框架，结合多种数据比较不同模型，用集成嵌套拉普拉斯近似推断。结果显示考虑空间依赖性可改进建模，随机偏微分方程公式表现更佳，该框架能增强预测等，是洪水保险中相关模型的首次应用。
中文摘要 AI 辅助
保险风险建模中的空间异质性通常用粗糙的区域结构表示，这可能掩盖对准确风险评估至关重要的精细尺度模式。本研究引入点参考贝叶斯框架，在投保人层面模拟索赔发生和严重程度，避免依赖预定义地理聚合。利用法国大型保险组合及高分辨率环境变量等，比较基准广义线性模型与多种离散贝叶斯规范及基于随机偏微分方程方法构建的连续索引高斯随机场。使用集成嵌套拉普拉斯近似进行推断。结果表明考虑空间依赖性显著改善发生建模，严重程度预测收益更有限。随机偏微分方程公式通过捕获次市政风险梯度等优于区域模型。通过以详细建筑层面属性为条件，隔离潜在空间效应贡献等。该框架除增强预测性能外，还提供连贯不确定性量化并支持尾部风险评估，是点参考随机偏微分方程模型在洪水保险中的首次应用，为定价和管理具有强空间结构的风险提供可扩展统计替代方案。
英文摘要
Spatial heterogeneity in insurance risk modelling is often represented using coarse areal structures, which can obscure fine-scale patterns critical for accurate risk assessment. This study introduces a point-referenced Bayesian framework to model claim occurrence and severity at the policyholder level, avoiding reliance on predefined geographic aggregation. Drawing on a large French insurance portfolio combined with high-resolution environmental variables, rainfall records, and institutional hazard maps, we compare a benchmark GLM with several discrete Bayesian specifications, including independent random effects, intrinsic conditional autoregressive (iCAR) and Besag-York-Mollie (BYM) models, and a continuously indexed Gaussian random field constructed using the stochastic partial differential equation (SPDE) approach. Inference is performed using Integrated Nested Laplace Approximation (INLA), enabling efficient estimation of latent spatial fields and non-linear covariate effects. Our results show that accounting for spatial dependence substantially improves occurrence modelling, while gains in severity prediction are more limited. The SPDE formulation further outperforms areal models by capturing sub-municipal risk gradients and reducing artefacts induced by arbitrary geographic partitioning. By conditioning on detailed building-level attributes, we isolate the contribution of latent spatial effects, refine the interpretation of observed covariates, and improve the allocation of risk premiums across the portfolio. In addition to enhanced predictive performance, the framework provides coherent uncertainty quantification and supports tail-risk assessment. To our knowledge, this is the first application of point-referenced SPDE models to flood insurance, offering a scalable statistical alternative for pricing and managing risks with strong spatial structure.
