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Minimizing the probability of lifetime ruin under stochastic volatility

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  • Bayraktar, Erhan
  • Hu, Xueying
  • Young, Virginia R.

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. 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

  • Bayraktar, Erhan & Hu, Xueying & Young, Virginia R., 2011. "Minimizing the probability of lifetime ruin under stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 194-206, September.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:194-206
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    References listed on IDEAS

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    1. 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.
    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. Mattias Jonsson & K. Ronnie Sircar, 2002. "Partial Hedging In A Stochastic Volatility Environment," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 375-409.
    4. 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.
    5. Erhan Bayraktar & Virginia R. Young, 2008. "Minimizing the Probability of Ruin when Consumption is Ratcheted," Papers 0806.2358, arXiv.org.
    6. 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.
    7. 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.
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    Cited by:

    1. 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.
    2. Erhan Bayraktar & Yuchong Zhang, 2014. "Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion," Papers 1402.1809, arXiv.org, revised Nov 2014.

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