Neural networks are advanced computer artificial intelligence that is able to capture and represent complex relationships. It can compare existing stock-trading patterns with previous situations, analyze all kind of indicators and eventually "learn" what works and what doesn't as the program digests more data. The true power and advantage of neural networks lies in their ability to digest a huge amount of data, find both linear and non-linear relationships from trading patterns, and make deep analytics that can never be accomplished by human analysts at the same time.
Neural networks are built into various sophisticated trading systems in wall street firms.
An expert system is a sophisticated computer program that can make intelligent or best possible decisions based on historical experience, accumulated knowledge and mathematics. Expert systems are suitable to handle extremely complex but specific problems, such as investment decisions, Stock/bond/currency trading, long-term weather forecast, and speech recognition etc.
Given enough data and computing power, an expert system can find the best possible solution via exhaustive search and comparison. IBM's Deep Blue(which defeated the reigning world's chess champion in 1997) is a perfect example that how smart and powerful an expert system can be.
Articles on the Applications of Artificial Intelligence in Wall Street
U.S.News: Investing with Neural Networks
U.S.News: Artificially intelligent investing
Books on the Applications of Neural Networks to the Financial World: