Additive portfolio improvement and utility-efficient payoffs

How can individual financial contracts be improved in an additive manner, such that any portfolio comprising improved contracts is at least as attractive as the portfolio of original contracts? We show that any additive procedure that improves contracts for all expected utility maximizers is a conditional expectation operator. Improved contracts are also attractive under robust Savage preferences. Furthermore, we generalize Bondarenko's definition of 'statistical arbitrage' and show that the improved contracts do not admit this kind of arbitrage.