Limit theorems and price changes in financial markets

We discuss the relation between limit theorems in probability theory and price change statistics in financial markets. An analysis of the published empirical results and theoretical models show that the problem of the statistical properties of price (or index) changes is still open. By using the limit theorems of probability theory and the current assumption that stock prices are well described by martingales, we point out that the probability density function (PDF) of price changes is expected to belong to theclass of infinitely divisible PDFs.