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Lifetime asset allocation with idiosyncratic and systematic mortality risks

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  • Yang Shen
  • Michael Sherris

Abstract

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.

Suggested Citation

  • Yang Shen & Michael Sherris, 2018. "Lifetime asset allocation with idiosyncratic and systematic mortality risks," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(4), pages 294-327, April.
    • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:4:p:294-327
    DOI: 10.1080/03461238.2017.1343749
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    Cited by:

    1. Ailing Gu & Xinya He & Shumin Chen & Haixiang Yao, 2023. "Optimal Investment-Consumption and Life Insurance Strategy with Mispricing and Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-19, September.
    2. Peng, Xingchun & Li, Baihui, 2023. "Optimal investment, consumption and life insurance purchase with learning about return predictability," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 70-95.

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