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.
@article{1029962818,
author = {Kramkov, D. and Schachermayer, W.},
title = {The asymptotic elasticity of utility functions and optimal
investment in incomplete markets},
journal = {Ann. Appl. Probab.},
volume = {9},
number = {1},
year = {1999},
pages = { 904-950},
language = {en},
url = {http://dml.mathdoc.fr/item/1029962818}
}
Kramkov, D.; Schachermayer, W. The asymptotic elasticity of utility functions and optimal
investment in incomplete markets. Ann. Appl. Probab., Tome 9 (1999) no. 1, pp. 904-950. http://gdmltest.u-ga.fr/item/1029962818/