Convergence of option rewards for Markov type price processes

A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process controlling the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the pay-off functions are assumed to depend on a perturbation parameter $\delta\geq0$ and to converge to the corresponding limit characteristics as $\delta\to0.$ Results about the convergence of reward functionals for American type options for perturbed processes are presented for models with continuous and discrete time as well as asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models.