We analyze financial markets in which agents face differential constraints on the set of assets in which they can trade. In particular, the assets available to each agent span a partition of the state space that can be strictly coarser than the partition spanned by the assets available in the market. We first show that the existence of differential constraints has an impact on prices and allocations as compared to a complete financial market with unconstrained agents. We consider the implications for survival, taking the work of Blume and Easley (2006) as a starting point. We show that whenever agents have identical correct beliefs and equal discount factors, and their partitions are nested, all agents survive. When agents have heterogeneous beliefs, differential constraints may allow agents with wrong beliefs to survive. Provided constraints are relevant (in a sense we define more precisely), the condition for an agent to survive is that his survival index is at least as large as that of the agents with finer partitions. We also study the impact of deregulation (an increase in the set of assets available to some agents). Unless the agent can adopt beliefs that are closer to the truth on the newly refined partition than those of less constrained agents, increasing his opportunities for trade might harm his chances for survival.