A generalization of Dybvig’s result on portfolio selection with intolerance for decline in consumption
In this note we show the following result of Dybvig (1995) is valid for a general von Neumann–Morgenstern utility function: for an agent who does not tolerate a decline in consumption, the optimal investment out of discretionary wealth (in excess of the perpetuity value of current consumption) in the risky asset does not depend on the risk aversion coefficient of her felicity function locally when she does not adjust her consumption. The homotheticity assumption is not required. An implication of our result is that if an economic agent exhibits non-time-separable preference due to intertemporal linkage of consumption, her risk-taking over a short time period can be independent of her felicity function.
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- Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," Review of Economic Studies, Oxford University Press, vol. 62(2), pages 287-313.
- Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
- Riedel, Frank, 2009.
"Optimal consumption choice with intolerance for declining standard of living,"
Journal of Mathematical Economics,
Elsevier, vol. 45(7-8), pages 449-464, July.
- Riedel, Frank, 2011. "Optimal consumption choice with intolerance for declining standard of living," Center for Mathematical Economics Working Papers 394, Center for Mathematical Economics, Bielefeld University.
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