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Modelling Outstanding Claims with Mixed Compound Processes in Insurance

机译：在保险中使用混合复合过程进行建模

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In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analyzed by exploiting the Fisher-Lange average cost method.
机译：在一般保险中，衡量未来亏损支付的不确定性和估算索赔储备金是争议的主要目标。为了处理这些棘手的任务，广泛的文献可用于确定性和随机方法，其中大部分是旨在直接建模整个索赔储备。本文通过扩展，非常一般和可重复的案例研究，我们通过归因于径流三角形的下部的每个单元来分析保留过程，该方法是复合混合泊松过程，校准了索赔和未来的数量平均成本和考虑到增量索赔之间的依赖。我们在分析上提供增量付款和总储备的时刻。此外，我们认为索赔储备的概率分布，这对于评估偿付能力II框架的风险储备资本要求是必要的。为了测试模型在不同情景，保险公司和业务范围下的影响，通过利用Fisher-Lange平均成本方法彻底分析了案例研究。

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