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Correspondence between lifetime minimum wealth and utility of consumption

  • Erhan Bayraktar

    ()

  • Virginia Young

    ()

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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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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  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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