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Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruin

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  • Erhan Bayraktar
  • Virginia R. Young

Abstract

In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.

Suggested Citation

  • Erhan Bayraktar & Virginia R. Young, 2012. "Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruin," Papers 1206.6268, arXiv.org.
    • Handle: RePEc:arx:papers:1206.6268
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    File URL: http://arxiv.org/pdf/1206.6268
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    References listed on IDEAS

    as
    1. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    2. 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.
    3. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
    4. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    5. 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.
    6. 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.
    7. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, July.
    8. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
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    Cited by:

    1. Peter Grandits, 2015. "An optimal consumption problem in finite time with a constraint on the ruin probability," Finance and Stochastics, Springer, vol. 19(4), pages 791-847, October.
    2. Dongchen Li & Virginia R. Young, 2020. "Maximizing expected exponential utility of consumption with a constraint on expected time in poverty," Annals of Finance, Springer, vol. 16(1), pages 63-99, March.
    3. Benjamin Avanzi & Lewis de Felice, 2023. "Optimal Strategies for the Decumulation of Retirement Savings under Differing Appetites for Liquidity and Investment Risks," Papers 2312.14355, arXiv.org, revised Mar 2024.
    4. Li, Danping & Li, Dongchen & Young, Virginia R., 2017. "Optimality of excess-loss reinsurance under a mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 82-89.

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