Frontiers of finance: Evolution and efficient markets

In this review article, we explore several recent advances in the quantitat ive modeling of financial markets. We begin with the Efficient Markets Hypo thesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical mo dels that are capable of rationalizing the empirical facts, others taking a completely different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological pe rspective and, specifically, within an evolutionary framework in which mark ets, instruments, institutions, and investors interact and evolve dynamical ly 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.