A rapidly growing area of mathematical finance is quantitative behavioral finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.
These include considering motivations beyond valuation considerations, and an asset base that is not infinite. The asset flow system of ordinary differential equations developed by Prof. Caginalp and collaborators in the 1990s has been an active part of this research at Pitt. These equations are being used to understand the dynamics and stability.
A related component involves large scale studies (e.g. over 100,000 data points) of market data that can be used to deduce underlying motivational effects. By extracting the valuation, recent studies have shown that momentum trading (buying on uptrend) plays a strong role, as do money supply, changes in volume and several other variable. Furthermore, with suitable modeling, one can deduce nonlinear effects. In particular, a recent uptrend that is too steep has a negative influence on prices. These topics have been the focus of the PhD thesis of Mark DeSantis at the University of Pittsburgh.