Gollier proposed in 2008 a model for the analysis of pension schemes that is helpful to focus attention on the impact of intergenerational risk sharing and on the role of the participation constraint. He uses the model to analyze the relative attractiveness of a collective scheme with respect to schemes that may be implemented by individuals for themselves. The analysis makes use of an assumption concerning the ownership rights of investment returns realized by generations that are between career start and retirement at the time of the transition from an individual to a collective system. The present paper investigates the consequences of adopting an alternative assumption. In a calibration exercise, the increase of the effective rate of return obtained by switching from an existing ‘autarky’ scheme to an infinite-horizon ‘collective’ scheme is found to be 8 basis points, as opposed to 72 basis points as reported by Gollier. Additionally, the effects are considered of changes in the specification of agents' preferences, aiming to express the specific nature of retirement income provision in the second pillar. The Black–Scholes assumptions are used to model the economic environment, so that many results can be obtained in closed form.

Gollier在2008年提出了一种养老金计划分析模型，该模型有助于将注意力集中在代际风险分担的影响和参与约束的作用上。他使用该模型来分析集体计划相对于个人可以自己实施的计划的相对吸引力。该分析利用了关于从个人向集体系统过渡时的职业生涯开始到退休之间的世代实现的投资回报的所有权的假设。本文研究采用替代假设的后果。在校准练习中，从现有的“自给自足”的方案转换为无限水平的“集体”方案所获得的有效收益率的增加被发现是8个基点，而Gollier报告的是72个基点。此外，考虑了代理人偏好规范变化的影响，目的是在第二个支柱中表达退休收入拨备的具体性质。Black-Scholes假设用于模拟经济环境，因此可以以封闭形式获得许多结果。