In this work we discuss a special kind of stochastic processesX=〖{X_t}〗_(〖t∈R〗_(≥0) ) that are of exceptional interest from both the theoretical ad the applied points of view. These processes are called Affine Processes, and are characterized by the fact that their characteristic function has the form of an exponential of an affine function, i.e. by 〖∅^x〗_X (u) |_t=E^x [e^(<X_(t ),u>) ]=e^(Φ(t,u)+<x,Ψ(t,u)>), Where the exponent Φ(t,u)+ <x,Ψ(t,u)> Is an affine function of its initial state x in the state-space E=〖R^m〗_(≥0)×R^n. The above expectation E^x is the expectation which respect to the ...