The asymptotic elasticity of utility functions and optimal investment in incomplete markets

Authors
Kramkov, D. Schachermayer, W.
Citation
D. Kramkov, et W. Schachermayer,, The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Annals of applied probability , 9(3), 1999, pp. 904-950
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
9
Issue
3
Year of publication
1999
Pages
904 - 950
Database
ACNP
SICI code
Abstract
The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.