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Minimizing Lifetime Poverty with a Penalty for Bankruptcy

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  • Asaf Cohen
  • Virginia R. Young

Abstract

We provide investment advice for an individual who wishes to minimize her lifetime poverty, with a penalty for bankruptcy or ruin. We measure poverty via a non-negative, non-increasing function of (running) wealth. Thus, the lower wealth falls and the longer wealth stays low, the greater the penalty. This paper generalizes the problems of minimizing the probability of lifetime ruin and minimizing expected lifetime occupation, with the poverty function serving as a bridge between the two. To illustrate our model, we compute the optimal investment strategies for a specific poverty function and two consumption functions, and we prove some interesting properties of those investment strategies.

Suggested Citation

  • Asaf Cohen & Virginia R. Young, 2015. "Minimizing Lifetime Poverty with a Penalty for Bankruptcy," Papers 1509.01694, arXiv.org.
    • Handle: RePEc:arx:papers:1509.01694
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    2. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2015. "Minimizing the expected lifetime spent in drawdown under proportional consumption," Finance Research Letters, Elsevier, vol. 15(C), pages 106-114.
    3. Erhan Bayraktar & Virginia R. Young, 2007. "Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin," Papers math/0703862, arXiv.org, revised Oct 2007.
    4. Bayraktar, Erhan & Young, Virginia R., 2016. "Optimally investing to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 1-10.
    5. Satya R. Chakravarty, 2009. "Inequality, Polarization and Poverty," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-79253-8, November.
    6. Erhan Bayraktar & S. David Promislow & Virginia R. Young, 2015. "Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(3), pages 224-236, July.
    7. Erhan Bayraktar & Yuchong Zhang, 2014. "Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion," Papers 1402.1809, arXiv.org, revised Nov 2014.
    8. Erhan Bayraktar & Virginia Young, 2007. "Correspondence between lifetime minimum wealth and utility of consumption," Finance and Stochastics, Springer, vol. 11(2), pages 213-236, April.
    9. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2016. "Minimizing the probability of lifetime drawdown under constant consumption," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 210-223.
    10. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    11. Erhan Bayraktar & Virginia Young, 2010. "Optimal investment strategy to minimize occupation time," Annals of Operations Research, Springer, vol. 176(1), pages 389-408, April.
    12. Bayraktar, Erhan & Promislow, S. David & Young, Virginia R., 2014. "Purchasing life insurance to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 204-216.
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