Quadratic Approximations of the Portfolio Selection Problem When the Means and Variances of Returns are Infinite

This paper derives quadratic approximations of the standard one-period portfolio selection model under the assumption that means and variances of returns are infinite. Samuelson [Samuelson, P. A. 1970. The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments. Rev. Econom. Stud.37 October.], among others, has derived mean-variance approximations when moments are finite; hence, this paper weakens conditions sufficient to obtain quadratic approximations.