Correspondence between Lifetime Minimum Wealth and Utility of Consumption
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number math/0703820.
Date of creation: Mar 2007
Date of revision:
Publication status: Published in Finance and Stochastics, 2007, Volume 11 (2), 213-236
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Web page: http://arxiv.org/
Other versions of this item:
- 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.
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- 91B - - - - - -
- 91B - - - - - -
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