In this article we solve the problem of maximizing the expected utility of future consumption and terminal wealth to determine the optimal pension or life-cycle fund strategy for a cohort of pension fund investors. The setup is strongly related to a DC pension plan where additionally (individual) consumption is taken into account. The consumption rate is subject to a time-varying minimum level and terminal wealth is subject to a terminal floor. Moreover, the preference between consumption and terminal wealth as well as the intertemporal coefficient of risk aversion are time-varying and therefore depend on the age of the considered pension cohort. The optimal consumption and investment policies are calculated in the case of a Black–Scholes financial market framework and hyperbolic absolute risk aversion (HARA) utility functions. We generalize Ye (American control conference, 2008) by adding an age-dependent coefficient of risk aversion and extend Steffensen (J Econ Dyn Control 35(5):659–667, 2011), Hentschel (Planning for individual retirement: optimal consumption, investment and retirement timing under different preferences and habit persistence. Ph.D. thesis, Ulm University, 2016) and Aase (Stochastics 89(1):115–141, 2017) by considering consumption in combination with terminal wealth and allowing for consumption and terminal wealth floors via an application of HARA utility functions. A case study on fitting several models to realistic, time-dependent life-cycle consumption and relative investment profiles shows that only our extended model with time-varying preference parameters provides sufficient flexibility for an adequate fit. This is of particular interest to life-cycle products for (private) pension investments or pension insurance in general.

在本文中，我们解决了使未来消费和终端财富的预期效用最大化的问题，从而确定了一批养老基金投资者的最佳养老金或生命周期基金策略。该设置与DC养老金计划密切相关，在DC养老金计划中还考虑了其​​他（个人）消费。消费率受制于随时间变化的最低水平，而终端财富则受制于终端楼层。此外，消费和终端财富之间的偏好以及风险规避的跨期系数是随时间变化的，因此取决于所考虑的养老金队列的年龄。在Black-Scholes金融市场框架和双曲线绝对风险规避（HARA）效用函数的情况下，计算出最佳的消费和投资政策。我们通过添加年龄相关的风险规避系数来概括Ye（美国控制会议，2008），并扩展Steffensen（J Econ Dyn Control 35（5）：659–667，2011），Hentschel（个人退休计划：最优消费，在考虑不同偏好和习惯的情况下的投资和退休时机（乌尔姆大学，2016年）和Aase（Stochastics 89（1）：115-141，2017年），将消费与终端财富结合起来考虑，并允许消费和退休。通过使用HARA实用程序功能来实现终端财富楼层。关于将多个模型拟合为现实的，与时间相关的生命周期消耗和相对投资概况的案例研究表明，只有我们的扩展模型具有随时间变化的偏好参数，才能为充分拟合提供足够的灵活性。