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Minimizing the Probability of Lifetime Ruin under Stochastic Volatility

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  • Erhan Bayraktar
  • Xueying Hu
  • Virginia R. Young

Abstract

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to include stochastic volatility in the risky asset's price process. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of going bankrupt. To solve this minimization problem, we use techniques from stochastic optimal control.

Suggested Citation

  • Erhan Bayraktar & Xueying Hu & Virginia R. Young, 2010. "Minimizing the Probability of Lifetime Ruin under Stochastic Volatility," Papers 1003.4216, arXiv.org, revised May 2011.
    • Handle: RePEc:arx:papers:1003.4216
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    References listed on IDEAS

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    1. 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.
    2. Erhan Bayraktar & Kristen Moore & Virginia Young, 2008. "Minimizing the Probability of Lifetime Ruin under Random Consumption," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(4), pages 384-400.
    3. 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.
    4. Kristen Moore & Virginia Young, 2006. "Optimal and Simple, Nearly Optimal Rules for Minimizing the Probability Of Financial Ruin in Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 145-161.
    5. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity‐Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671, October.
    6. 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.
    7. Mattias Jonsson & K. Ronnie Sircar, 2002. "Partial Hedging In A Stochastic Volatility Environment," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 375-409, October.
    8. 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.
    9. Erhan Bayraktar & Virginia Young, 2008. "Minimizing the Probability of Ruin When Consumption is Ratcheted," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(4), pages 428-442.
    10. 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.
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    Cited by:

    1. Liang, Xiaoqing & Young, Virginia R., 2023. "Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 80-96.
    2. Wang, Ting & Young, Virginia R., 2012. "Maximizing the utility of consumption with commutable life annuities," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 352-369.
    3. Erhan Bayraktar & Yuchong Zhang, 2014. "Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion," Papers 1402.1809, arXiv.org, revised Nov 2014.
    4. Tong Qian & Cuixia Chen & Weijun Yin & Bing Liu, 2024. "Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    5. Xiaoqing Liang & Virginia R. Young, 2020. "Minimizing the Probability of Lifetime Exponential Parisian Ruin," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1036-1064, March.

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