Jump systems with the mean-reverting gamma-process and convergence of the numerical approximation.

In this paper, a class of jump systems with the mean-reverting gamma-process are considered in finance. The analytical properties including the positivity, boundedness and pathwise estimations of the solution are discussed. Moreover, the authors show that the Euler-Maruyama approximate solutions converge to the true solutions in probability. Finally, the authors apply the convergence to examine a bond and a path-dependent option price in the financial pricing.