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Around the Life Cycle: Deterministic Consumption-Investment Strategies

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  • Marcus C. Christiansen
  • Mogens Steffensen

Abstract

We study a classical continuous-time consumption-investment problem of a power utility investor with deterministic labor income with the important feature that the consumption-investment process is constrained to be deterministic. This is motivated by the design of modern pension schemes of defined contribution type where, typically, the savings rate is constant and the proportional investment in growth stocks is a function of age or time-to-retirement, a so-called life-cycle investment strategy. We derive and study the optimal behavior corresponding to the optimal product design within this realistic family of products with deterministic decision profiles. We also propose a couple of suboptimal deterministic strategies inspired from the optimal stochastic strategy and compare the optimal stochastic control, the optimal deterministic control, and these suboptimal deterministic controls. The conclusion is that only little is lost by constraining to deterministic strategies and only little is lost by implementing the suboptimal simple explicit strategies rather than the optimal one we derive.

Suggested Citation

  • Marcus C. Christiansen & Mogens Steffensen, 2018. "Around the Life Cycle: Deterministic Consumption-Investment Strategies," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 491-507, July.
    • Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:491-507
    DOI: 10.1080/10920277.2018.1450156
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    Cited by:

    1. Khemka, Gaurav & Steffensen, Mogens & Warren, Geoffrey J., 2021. "How sub-optimal are age-based life-cycle investment products?," International Review of Financial Analysis, Elsevier, vol. 73(C).
    2. Chavez-Bedoya, Luis & Castaneda, Ranu, 2021. "A benchmarking approach to track and compare administrative charges on flow and balance in individual account pension systems," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 7-23.
    3. S{o}ren Fiig Jarner, 2022. "Strategic mean-variance investing under mean-reverting stock returns," Papers 2201.05375, arXiv.org.

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