Optimal consumption and investment under time-varying relative risk aversion
We consider the continuous time consumption-investment problem originally formalized and solved by Merton in case of constant relative risk aversion. We present a complete solution for the case where relative risk aversion with respect to consumption varies with time, having in mind an investor with age-dependent risk aversion. This provides a new motivation for life-cycle investment rules. We study the optimal consumption and investment rules, in particular in the case where the relative risk aversion with respect to consumption is increasing with age.
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- Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
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- repec:kap:iaecre:v:15:y:2009:i:4:p:369-377 is not listed on IDEAS
- Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
- Aase, Knut K., 2009. "The investment horizon problem: A resolution," Discussion Papers 2009/7, Department of Business and Management Science, Norwegian School of Economics.
- Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
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