Correspondence between Lifetime Minimum Wealth and Utility of Consumption

Details Correspondence between Lifetime Minimum Wealth and Utility of Consumption Correspondence between Lifetime Minimum Wealth and Utility of Consumption

2007-03-27

arxiv.org/abs/math/0703820v1

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

Mathematics

Optimization and Control

Scientific paper

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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