Agents with incorrect beliefs can survive and even prosper through speculation in financial markets, depending on how complete the markets are. In a model with incomplete markets, over-optimistic agents can thrive by taking risks, but end up with less wealth in the long run when markets are more complete. Tighter margin requirements can protect optimists' wealth but also increase asset price volatility. The findings suggest that the level of market completeness plays a crucial role in determining the financial outcomes of agents with different beliefs.