Since the mid 1990s some European countries (including Italy) implemented a Notional Defined Contribution (NDC) pension system. Such a system is based on pay-as-you-go funding, while the pension amount is a function of the individual lifelong contribution. Despite many appealing features, the NDC system presents some drawbacks: first, it is vulnerable to demographic and economic shocks compromising the financial sustainability; second, it could fail to guarantee adequate pension benefits to pensioners. In order to reduce the first limit, automatic balance mechanisms (ABMs) have been proposed in literature and also implemented in Sweden, while solutions that combine financial sustainability and social adequacy have been applied only in a pay-as-you-go point system. The aim of this paper is to insert into the Italian NDC architecture ABMs that preserve social adequacy under financial sustainability constraints. Godinez-Olivares et al. (Insur Math Econ 69:117–126, 2016) built ABMs for a Defined Benefit pension system using nonlinear optimization techniques to calculate the optimal paths of the control variables representing the main drivers of the system: contribution rate, retirement age and indexation of pensions. Following this line of research, we have developed a nonlinear optimization model for the Italian NDC system based on three control variables: pensions indexation, notional rate and contribution rate. The objective function considers both social adequacy and contribution rate sustainability, under liquidity and sustainability constraints. In the numerical application we apply the model to the Italian pension system and test the sensitivity of the results to different economic scenarios and objective function parameters.

中文翻译：

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保证社会充足性和财务可持续性的名义固定缴款养老金系统的自动平衡机制：在意大利养老金系统中的应用

自 1990 年代中期以来，一些欧洲国家（包括意大利）实施了名义固定缴款 (NDC) 养老金制度。这种制度是基于现收现付的资金，而养老金金额是个人终身贡献的函数。尽管有许多吸引人的特点，但 NDC 系统也存在一些缺点：首先，它容易受到影响财务可持续性的人口和经济冲击；其次，它可能无法保证养老金领取者获得足够的养老金福利。为了减少第一限制，文献中提出了自动平衡机制（ABMs）并在瑞典实施，而结合财务可持续性和社会充足性的解决方案仅应用于现收现付点系统。本文的目的是将 ABM 插入意大利 NDC 架构中，以在财务可持续性约束下保持社会充足性。戈迪内斯-奥利瓦雷斯等人。(Insur Math Econ 69:117–126, 2016) 使用非线性优化技术为固定收益养老金系统构建 ABM，以计算代表系统主要驱动因素的控制变量的最佳路径：缴费率、退休年龄和养老金指数化. 遵循这一研究路线，我们基于三个控制变量为意大利 NDC 系统开发了非线性优化模型：养老金指数化、名义费率和缴费率。在流动性和可持续性约束下，目标函数同时考虑了社会充足性和缴费率的可持续性。