  In this paper, we consider the generalized Ait-Sahaliz interest rate model
with Poisson jumps in finance. The analytical properties including the
positivity, boundedness and pathwise asymptotic estimations of the solution to
the model are investigated. Moreover, we prove that the Euler-Maruyama (EM)
numerical solutions will converge to the true solution in probability. Finally,
under assumption that the interest rate or the asset price is governed by this
model, we apply the EM solutions to compute some financial quantities.
