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.
"The asymptotic elasticity of utility functions and optimal investment in incomplete markets." Ann. Appl. Probab. 9 (3) 904 - 950, August 1999. https://doi.org/10.1214/aoap/1029962818