Optimal contingent claims

Given a particular market variable, which could be finite dimensional (e.g., a price vector of a collection of stocks) or infinite dimensional (e.g., a price trajectory of some security over some period of time), we find the unique optimal European claim contingent on that variable in the sense that, for a given price and risk tolerance level, this claim has the highest expected return possible. The optimal contingent claims seem to be attractive investment instruments and are proposed for trade in derivatives markets.