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Correspondence between lifetime minimum wealth and utility of consumption

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  • Erhan Bayraktar

    ()

  • Virginia Young

    ()

Abstract

We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval $O$ in wealth space. To answer this question, we equate the two investment strategies and show that if the individual consumes at the same rate in both problems -- the consumption rate is a control in the problem of maximizing utility -- then the investment strategies are equal only when the consumption function is linear in wealth on $O$, a rather surprising result. It, then, follows that the corresponding investment strategy is also linear in wealth and the implied utility function exhibits hyperbolic absolute risk aversion.

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File URL: http://hdl.handle.net/10.1007/s00780-007-0035-7
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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 11 (2007)
Issue (Month): 2 (April)
Pages: 213-236

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Handle: RePEc:spr:finsto:v:11:y:2007:i:2:p:213-236

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Related research

Keywords: Optimal control; Probability of ruin; Utility of consumption; Investment/consumption decisions; G11; C61; 91B28; 91B42;

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  1. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
  2. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
  3. Milevsky, Moshe Arye & Ho, Kwok & Robinson, Chris, 1997. " Asset Allocation via the Conditional First Exit Time or How to Avoid Outliving Your Money," Review of Quantitative Finance and Accounting, Springer, vol. 9(1), pages 53-70, July.
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Cited by:
  1. Bayraktar, Erhan & Young, Virginia R., 2008. "Maximizing utility of consumption subject to a constraint on the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(4), pages 204-212, December.
  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.
  3. Erhan Bayraktar & Yuchong Zhang, 2014. "Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion," Papers 1402.1809, arXiv.org.
  4. Petrichev, Konstantin & Thorp, Susan, 2008. "The private value of public pensions," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1138-1145, June.
  5. Erhan Bayraktar, 2007. "Minimizing the Lifetime Shortfall or Shortfall at Death," Papers math/0703824, arXiv.org.
  6. Bayraktar, Erhan & Young, Virginia R., 2008. "Mutual fund theorems when minimizing the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(2), pages 69-78, June.
  7. Nielsen, Peter Holm & Steffensen, Mogens, 2008. "Optimal investment and life insurance strategies under minimum and maximum constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 15-28, August.
  8. Erhan Bayraktar & Virginia R. Young, 2008. "Minimizing the Probability of Ruin when Consumption is Ratcheted," Papers 0806.2358, arXiv.org.

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