Optimal life-cycle consumption and investment decisions under age-dependent risk preferences

TL;DR

This paper develops a model for optimal life-cycle investment and consumption decisions considering age-dependent risk preferences, incorporating floors and time-varying utility parameters, within a Black-Scholes market framework.

Contribution

It extends existing models by adding age-dependent risk aversion and consumption features, providing a more flexible framework for pension fund strategies.

Findings

The extended model fits realistic life-cycle profiles better.

Time-varying preferences improve model flexibility.

Application to pension products demonstrates practical relevance.

Abstract

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 (2008) (2008 American Control Conference, 356-362) by adding an age-dependent coefficient of risk aversion and extend Steffensen (2011) (Journal of Economic Dynamics and Control, 35(5), 659-667), Hentschel (2016) (Doctoral dissertation, Ulm University) and Aase (2017) (Stochastics, 89(1), 115-141) 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.