Optimal Life-Cycle Consumption and Investment Decisions Under Age-Dependent Risk Preferences

39 Pages Posted: 21 Nov 2018 Last revised: 31 Jul 2020

See all articles by Andreas Lichtenstern

Andreas Lichtenstern

Technische Universität München (TUM) - Chair of Mathematical Finance

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance

Date Written: October 26, 2018

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.

Keywords: optimal life-cycle consumption and investment, time-varying risk aversion, HARA utility function, martingale method

JEL Classification: C61, G11

Suggested Citation

Lichtenstern, Andreas and Shevchenko, Pavel V. and Zagst, Rudi, Optimal Life-Cycle Consumption and Investment Decisions Under Age-Dependent Risk Preferences (October 26, 2018). A. Lichtenstern, P.V.Shevchenko, R. Zagst (2020). Optimal life-cycle consumption and investment decisions under age-dependent risk preferences. Mathematics and Financial Economics. DOI 10.1007/s11579-020-00276-9., Available at SSRN: https://ssrn.com/abstract=3274598 or http://dx.doi.org/10.2139/ssrn.3274598

Andreas Lichtenstern (Contact Author)

Technische Universität München (TUM) - Chair of Mathematical Finance ( email )

Parkring 11
Garching-Hochbrueck, 85748
Germany

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance ( email )

Parkring 11
Garching-Hochbrueck, 85748
Germany
+49 89 289 17400 (Phone)

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