Household investment-consumption-insurance policies under the age-dependent risk preferences

Abstract

In this paper, we examine the optimal investment-consumption-insurance policies for a wage earner with time-varying risk preferences. The wage earner's objective is to find the optimal investment-consumption-insurance strategies that maximise the expected discounted utilities from intertemporal consumption, legacy and terminal wealth over the uncertain lifetime horizon. Similar to Lichtenstern et al. [Optimal life-cycle consumption and investment decisions under age-dependent risk preferences. Mathematics and Financial Economics, 15, 275–313], by using a separation approach, the problem is divided into two sub-problems, including the consumption-legacy problem and the terminal wealth-only problem. For each sub-problem, the analytical expressions for the optimal strategies and value functions are derived by using the martingale method. In such a way, we obtain the optimal strategies for the original problem by merging the solutions of the two individual problems. Finally, we conduct some numerical experiments to illustrate the effects of some parameters on the optimal strategies and obtain some economic insights.

Keywords:

• Life insurance
• consumption
• investment
• age-dependent risk aversion
• martingale method

Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable feedback that helped significantly improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that, the original optimisation problem can also be divided into the another two sub-problems: the consumption-only problem and the legacy-terminal wealth problem. However, it is hard to obtain the closed-form of the Lagrange multiplier in the second sub-problem because of the effects of the risk preference parameter $b(t)$.

Additional information

Funding

This work was supported by the 111 Project [grant number B14019], Anhui Provincial Natural Science Foundation [grant number 2108085QG304], Natural Science research project of Higher education in Anhui Province [grant number KJ2021A0104] and the National Natural Science Foundation of China [grant numbers 12101270, 12071147, 11971034].