# The Expected Utility of Portfolios of Assets

By Lars Tyge Nielsen

Journal of Mathematical Economics 22 (1993), 439-461

### Abstract

This paper describes two models of asset markets and portfolio choice: one where the von Neumann-Morgenstern utility function is defined on the nonnegative real line and short-selling is not allowed, and one where the von Neumann-Morgenstern utility function is defined on the entire real line and short-selling may be possible. A number of properties of the derived utility function for portfolios, needed in demand and equilibrium analysis, are investigated with particular attention to the possibility that the von Neumann- Morgenstern utility function may be unbounded below and that the derived (expected) utility of some portfolios may be negative infnity.