Correspondence between lifetime minimum wealth and utility of consumption
- 123 Downloads
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.
KeywordsOptimal control Probability of ruin Utility of consumption Investment/consumption decisions
Jel ClassificationG11 C61
Mathematics Subject Classification (2000)91B28 91B42
Unable to display preview. Download preview PDF.
- 1.Al-Gwaiz M.A. (1992). Theory of Distributions. Monographs and Textbooks in Pure and Applied Mathematics 159. Marcel Dekker, New York Google Scholar
- 3.Bayraktar, E., Young, V.R.: Minimizing the lifetime shortfall or shortfall at death. Working Paper, Department of Mathematics, University of Michigan (2005). http://www.math.lsa. umich.edu/∼erhan/shortfall.pdfGoogle Scholar
- 4.Bayraktar, E., Young, V.R.: Minimizing the probability of lifetime ruin under borrowing constraints. Insur. Math. Econ. (to appear 2006)Google Scholar
- 16.Merton R.C. (1992). Continuous-Time Finance (revised edition). Blackwell, Cambridge Google Scholar