In short, Econophysics wants to solve problems in economics applying methods from physics. One driving force behind econophysics was the emergent availability of a huge amount of data. Basic tools are probabilistic and statistical methods often taken from statistical physics. Moreover, IMO, attempts to use the theory of complex systems.
Working in quantitative finance, we know in depth that there are other tools from stochastic processes for pricing and risk analysis of financial instruments, analogies between financial theory and diffusion theory. The stochastic differential equations are often transformed into partial differential equations and depending on the deal types and contract features it is essential to have the right backwards or forward solvers and to treat the ill-posed inverse problem of calibration correctly - in UnRisk we worked for perfection of such solvers.
However, derivatives and risk analytics is characterized by the influence of a few factors (dominantly volatility of underlyings, correlations, ...), high dimensions come from the path dependence.
To study, say, market behavior or understanding systemic risk insights from the physical world can help, especially from systems in which networks of interacting units produce radical collective behavior.
Things like co-movements of, say, financial instruments are important - it is, for example, quite intuitive that in a panic co-movement increases - a stock market panic is like an avalanche where exogenous control becomes less important compared to streamline interactions within the network.
Mathematica 8 is fit for the petabyte age. It can manage massive data and has a vast variety of core algorithms related to probability and statistics and they become even stronger when intelligently combined with the many symbolic and numerical solvers. Methods that are only partially implemented or not covered can be easily extended or added. And we have the mlf that adds multi-strategy, multi-method machine learning.
We at uni software plus, have passionately worked in quantitative finance, data analysis and machine learning and we have extended our team with a theoretical physicist, teacher of an econophysics course, recently.
What have all our innovations, for over 20 years now, in common? Mathematica.
Econophysics is a field, where we get in quickly. It needs packaging an partnering.