  In this paper we model benchmark beating with the increasing convex order
(ICX order). The mean constraint in the mean-variance theory of portfolio
selection can be regarded as beating a constant. We then investigate the
problem of minimizing the variance of a portfolio with ICX order constraints,
based on which we also study the problem of beating-performance-variance
efficient portfolios. The optimal and efficient portfolios are all worked out
in closed form for complete markets.
