In this paper, we revisit pricing contingent claims in incomplete markets. While a lot have been done on pricing in incomplete markets, there is still a gap on the categorization of the payoffs. Some contingent claims are attainable while others will not be attainable. We address the question of which contingent claims belong to each group. We also propose a generalization of the equivalent martingale measures used for pricing, a generalization which includes those studied so far. We also provide some examples of how to price in each class and introduce important definitions.
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