Simple Market Structures are Incomplete

We propose a model of categorization in financial markets where states are defined by payoff‐relevant variables, but all securities are measurable with respect to strict subsets of these variables. This limits insurance against variable interactions: no combination of securities can compensate the absence of an instrument targeting a given set of variables. We provide a decomposition result that identifies the uninsurable component of income risk for any market. We derive a lower bound on the number of securities required for efficiency. Using the same techniques, we characterize the payoff space when individuals condition only on a personal set of variables.