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Correspondence between Lifetime Minimum Wealth and Utility of Consumption

24 Pages Posted: 28 May 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: December 16, 2006

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.

Keywords: Optimal control, Probability of ruin, Utility of consumption, Investment/consumption decisions

JEL Classification: G11, C61

Suggested Citation

Bayraktar, Erhan and Young, V.R., Correspondence between Lifetime Minimum Wealth and Utility of Consumption (December 16, 2006). Finance Stochastics, Vol. 11, 2007. Available at SSRN: https://ssrn.com/abstract=2785660

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Virginia R. Young

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

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