Asset prices are forward looking. This evidence implies that prices of financial assets are essentially determined by the traders expectations about future prices. Another evidence about asset prices is that these do not seem to follow a predictable pattern over time; we observe periods of high volatility, periods of large negative returns and periods of observation clustering, without noticing any kind of regular pattern. How can one conciliate the formation of expectations with unpredictable erratic behavior? The ‘routes to randomness’ strand of literature has tried to answer the previous question in the last few years. Two conditions are essential to explain asset price unpredictability. (1) agents have different beliefs about future prices, (2) agents follow a rule of bounded rationality, under which they can change the way they form expectations, but such change does not occur instantly and permanently. In this paper the bounded rationality heterogeneous agents setup concerning asset prices is adapted to a continuous-time framework and general conditions conducting to erratic price behavior are presented and discussed.

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