In this paper a random discrete mathematical population model of immigration is constructed using not only rational factors as the gradient of economy level among the host and issuing countries, the geography, or the regulation laws, but also hidden intentional factors such as political interests of governments, or the business of smuggling of migrants by mafias, which use the immigration practically as a weapon. These non-rational factors are modeled as sudden random arrival flow waves represented by a Poisson distribution. The period of study is short in order to make reliable the economic forecast of the next years. Although the study is focused in Spain, the approach is exportable to other geographic areas by adapting the data. Results are applied to predict the necessary national budget of the host country to afford this social phenomenon.

In this paper we propose a numerical method for American multi-asset options under jump-diffusion model based on the combination of the exponential time differencing (ETD) technique for the differential operator and Gauss-Hermite quadrature for the integral term. In order to simplify the computational stencil and improve characteristics of the ETD-scheme mixed derivative eliminating transformation is applied. The results are compared with recently proposed methods.