For all practical purposes, then, market prices behave as though all traders were pursuing their self-interest with complete information and rationality.
On October 19, 1987 the Dow Jones average plunged over 20% in a single day, as many smaller stocks suffered deeper losses.
The crash of 1987 provided a puzzle and challenge to most economists who had believed that such volatility should not exist in an age when information and capital flows are much more efficient than they were in the 1920s.
Meanwhile, in the US the growth of new technology, particularly the internet, spawned a new generation of high tech companies, some of which became publicly traded long before any profits.
These large bubbles and crashes in the absence of significant changes in valuation cast doubt on the assumption of efficient markets that incorporate all public information accurately.
This line of reasoning has also been confirmed in several studies (e.g., Jeffrey Pontiff [3]), of closed-end funds which trade like stocks, but have a precise valuation that is reported frequently.
These experiments (in collaboration with Gerry Suchanek, Arlington Williams and David Porter and others) featuring participants trading an asset defined by the experimenters on a network of computers.
The challenge of using these ideas to forecast price dynamics in financial markets has been the focus of some of the recent work that has merged two different mathematical methods.
In his 2006 PhD thesis,[7] Duran examined 130,000 data points of daily prices for closed-end funds in terms of their deviation from the net asset value (NAV).
These precursors may suggest that an underlying cause of these large moves—in the absence of significant change in valuation—may be due to the positioning of traders in advance of anticipated news.
If the positive news does not materialize they are inclined to sell in large numbers, thereby suppressing the price significantly below the previous levels.
Research continues on efforts to optimize the parameters of the asset flow equations in order to forecast near term prices (see Duran and Caginalp [8]).
Duran [9] studied the stability analysis of the solutions for the dynamical system of nonlinear AFDEs in R^4, in three versions, analytically and numerically.