The main reason for the complexity of financial systems is caused by the fact that they represent derived processes. The first order proces is the real world, real time society in all its complexity. The economic systems are a first order derivate. The financial systems are but a third order derivate.
The main reason for the complexity of financial systems is caused by the fact that they represent derived processes. The first order proces is the real world,
Information-based complexity (IBC) studies optimal algorithms and computational complexity for the continuous problems that arise in physical science, economics, engineering, and mathematical finance.
IBC has studied such continuous problems as path integration, partial differential equations, systems of ordinary differential equations, nonlinear equations, integral equations, fixed points, and very-high-dimensional integration.
All these problems involve functions of a real or complex variable.
Since one can never obtain a closed-form solution to the problems of interest one has to settle for a numerical solution.
Since a function of a real or complex variable cannot be entered into a digital computer, the solution of continuous problems involves partial information.
To give a simple illustration, in the numerical approximation of an integral, only samples of the integrand at a finite number of points are available.
In the numerical solution of partial differential equations the functions specifying the boundary conditions and the coefficients of the differential operator can only be sampled.
Furthermore, this partial information can be expensive to obtain.
Finally the information is often contaminated by noise.
