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Collectivised Pension Investment with Exponential Kihlstrom--Mirman Preferences

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  • John Armstrong
  • Cristin Buescu

Abstract

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We give a numerical algorithm to compute the optimal investment-consumption strategy for an infinite collective of identical investors with exponential Kihlstrom--Mirman preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our algorithm can also be applied to an individual investor. We derive an analytic formula for the optimal consumption in the special case of an individual who chooses not to invest in the financial markets. We prove that our problem formulation for a fund with an infinite number of members is a good approximation to a fund with a large, but finite number of members.

Suggested Citation

  • John Armstrong & Cristin Buescu, 2019. "Collectivised Pension Investment with Exponential Kihlstrom--Mirman Preferences," Papers 1911.02296, arXiv.org, revised Nov 2019.
    • Handle: RePEc:arx:papers:1911.02296
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    References listed on IDEAS

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    1. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    2. John Armstrong & Cristin Buescu, 2019. "Collectivised Pension Investment with Homogeneous Epstein-Zin Preferences," Papers 1911.10047, arXiv.org.
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    Cited by:

    1. John Armstrong & Cristin Buescu & James Dalby & Rohan Hobbs, 2025. "Machine-learning a family of solutions to an optimal pension investment problem," Papers 2511.07045, arXiv.org.
    2. John Armstrong & Cristin Buescu, 2020. "Asymptotically Optimal Management of Heterogeneous Collectivised Investment Funds," Papers 2004.01506, arXiv.org.

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