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The book deals with the asymptotic behaviour of stochastic difference and functional differential equations of Ito type. The equations have a form which make them suitable to model financial markets in which agents use past prices. The main results of the time sysyetms concern the almost sure largest fluctuations of the cumulative returns. These results are robust to the time-discretisation of the process and to the presence of non-linearities in the traders' demand schedules. The conditions for, and dynamics in, a market experiencing a bubble or crash are also described. Numerical methods which both minimise error and preserve the features of the underlying continuous equation are studied and the methods are simulated on computer.