Mathematics – Optimization and Control
Scientific paper
2007-03-27
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.
Bayraktar Erhan
Young Virginia R.
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