Correspondence between Lifetime Minimum Wealth and Utility of Consumption

Erhan Bayraktar and Virginia R. Young

Papers from arXiv.org

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.

Date: 2007-03
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Citations: View citations in EconPapers (19)

Published in Finance and Stochastics, 2007, Volume 11 (2), 213-236

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Journal Article: Correspondence between lifetime minimum wealth and utility of consumption (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:math/0703820

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