  This paper studies the topic of cost-efficiency in incomplete markets. A
payoff is called cost-efficient if it achieves a given probability distribution
at some given investment horizon with a minimum initial budget. Extensive
literature exists for the case of a complete financial market. We show how the
problem can be extended to incomplete markets and how the main results from the
theory of complete markets still hold in adapted form. In particular, we find
that in incomplete markets, the optimal portfolio choice for non-decreasing
preferences that are diversification-loving (a notion introduced in this paper)
must be "perfectly" cost-efficient. This notion of perfect cost-efficiency is
shown to be equivalent to the fact that the payoff can be rationalized, i.e.,
it is the solution to an expected utility problem.
