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Mutual Fund Theorems when Minimizing the Probability of Lifetime Ruin

  • Erhan Bayraktar
  • Virginia R. Young

We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random consumption. The striking result is that we obtain two-fund theorems despite the additional source of randomness from consumption.

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File URL: http://arxiv.org/pdf/0705.0053
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Paper provided by arXiv.org in its series Papers with number 0705.0053.

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Date of creation: Apr 2007
Date of revision: Mar 2008
Handle: RePEc:arx:papers:0705.0053
Contact details of provider: Web page: http://arxiv.org/

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  1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  2. Erhan Bayraktar & Virginia R. Young, 2007. "Minimizing the Probability of Lifetime Ruin under Borrowing Constraints," Papers math/0703850, arXiv.org.
  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. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
  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. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
  7. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
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