This paper introduces a unified micro-level stochastic framework for the joint modeling of loss reserves (RBNS), incurred but not reported (IBNR) reserves, and unearned premium risk under dependence, inflation, and discounting. The proposed framework accommodates interactions between indemnities, expenses, reporting delays, and settlement delays, while allowing for flexible parametric dependence structures and dynamic financial adjustments. An Aggregate Trend Renewal Process (ATRP) is used as one possible implementation of the joint model for payments, expenses, and delays; however, the methodological contribution of the paper lies in the unified micro-level reserving architecture rather than in the ATRP itself. The framework produces forward-looking reserve and premium risk measures with direct applications to pricing, reserving, and capital management. We implement the framework using an aggregate trend renewal process at the individual claim level, which can be applied to the usual run-off triangle to obtain predictions for each accident-development year. Closed-form expressions for the first two raw and joint conditional moments of predicted payments are derived, together with approximations of their distribution functions. A detailed case study on medical malpractice insurance illustrates the practical relevance of the approach and its calibration on real-world data. We also investigate data heterogeneity, parameter uncertainty, distributional approximations, premium risk, UPR sensitivity to operational delays and inflation, and risk capital implications under alternative assumptions. The results highlight the advantages of unified micro-level modeling for dynamic liability and premium risk assessment in long-tailed lines of business.

翻译：本文提出了一种统一的微观层面随机框架，用于在相依性、通胀和折现条件下联合建模损失准备金（RBNS）、已发生未报告（IBNR）准备金及未满期保费风险。该框架能够容纳赔款、费用、报告延迟和结案延迟之间的相互作用，同时允许灵活的参数相依结构及动态财务调整。聚合趋势更新过程（ATRP）被用作支付、费用与延迟联合模型的一种可能实现方式；然而，本文的方法论贡献在于统一的微观准备金架构，而非ATRP本身。该框架生成具有前瞻性的准备金与保费风险度量，可直接应用于定价、准备金计提和资本管理。我们在个体索赔层面使用聚合趋势更新过程实施该框架，可应用于常规流量三角形以获得各事故-进展年度的预测值。推导了预测支付额的前两阶原始条件矩与联合条件矩的闭式表达式，及其分布函数的近似形式。一项针对医疗责任保险的详细案例研究说明了该方法的实际相关性及其在真实数据上的校准过程。我们还研究了数据异质性、参数不确定性、分布近似、保费风险、未满期保费对运营延迟与通胀的敏感性，以及不同假设下的风险资本影响。结果凸显了统一微观建模在长尾业务中对动态负债与保费风险评估的优势。