One of the challenges in the healthcare sector is making accurate forecasts across insurance years for claims reserve. Healthcare claims present huge variability and heterogeneity influenced by random decisions of the courts and intrinsic characteristics of the damaged parties, which makes traditional methods for estimating reserves inadequate. We propose a new methodology to estimate claim reserves in the healthcare insurance system based on generalized linear models using the Overdispersed Poisson distribution function. In this context, we developed a method to estimate the parameters of the quasi-likelihood function using a Gauss–Newton algorithm optimized through a genetic algorithm. The genetic algorithm plays a crucial role in glimpsing the position of the global minimum to ensure a correct convergence of the Gauss–Newton method, where the choice of the initial guess is fundamental. This methodology is applied as a case study to the healthcare system of the Tuscany region. The results were validated by comparing them with state-of-the-art measurement of the confidence intervals of the Overdispersed Poisson distribution parameters with better outcomes. Hence, local healthcare authorities could use the proposed and improved methodology to allocate resources dedicated to healthcare and global management.

中文翻译：

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医疗保健系统中的随机索赔准备金：应用于意大利数据的方法

医疗保健行业面临的挑战之一是对各个保险年度的索赔准备金进行准确预测。受法院随机判决和受损方固有特征的影响，医疗保健索赔呈现出巨大的可变性和异质性，这使得传统的准备金估算方法不够充分。我们提出了一种新的方法来估计医疗保险系统中的索赔准备金，该方法基于使用过度分散泊松分布函数的广义线性模型。在这种背景下，我们开发了一种使用通过遗传算法优化的高斯-牛顿算法来估计拟似然函数参数的方法。遗传算法在查看全局最小值的位置以确保高斯-牛顿方法的正确收敛方面发挥着至关重要的作用，其中初始猜测的选择至关重要。该方法作为托斯卡纳地区医疗保健系统的案例研究。通过将结果与最先进的过度分散泊松分布参数置信区间测量进行比较，对结果进行了验证，结果更好。因此，地方医疗保健当局可以使用拟议的和改进的方法来分配专门用于医疗保健和全球管理的资源。