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Minimizing the Probability of Lifetime Ruin under Random Consumption

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  • Erhan Bayraktar
  • Kristen Moore
  • Virginia Young

Abstract

We determine the optimal investment strategy in a financial market for an individual whose random consumption is correlated with the price of a risky asset. Bayraktar and Young consider this problem and show that the minimum probability of lifetime ruin is the unique convex, smooth solution of its corresponding Hamilton-Jacobi-Bellman equation. In this paper we focus on determining the probability of lifetime ruin and the corresponding optimal investment strategy. We obtain approximations for the probability of lifetime ruin for small values of certain parameters and demonstrate numerically that they are reasonable ones. We also obtain numerical results in cases for which those parameters are not small.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:4:p:384-400
    DOI: 10.1080/10920277.2008.10597531
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    Cited by:

    1. Wang, Ting & Young, Virginia R., 2012. "Optimal commutable annuities to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 200-216.
    2. 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.

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