  In this review article we explore several recent advances in the quantitative
modeling of financial markets. We begin with the Efficient Markets Hypothesis
and describe how this controversial idea has stimulated a number of new
directions of research, some focusing on more elaborate mathematical models
that are captable of rationalizing the empirical facrts, others taking a
completely different different tack in rejecting rationality altogether. One of
the most promising directions is to view financial markets from a biological
perspective and, specifically, with an evolutionary framework in which markets,
instruments, institutions, and investors interact and evolve dynamically
according to the "law" of economic selection. Under this view, financial agents
compete and adapt, but they do not necessarily do so in an optimal fashion.
Evolutionary and ecological models of financial markets is truly a new frontier
whose exploration has just begun.
