The range of american contingent claims prices in the jump-diffusion model

The problem of valuation of American-type contingent claims in incomplete financial market models is considered. Market models are defined by stochastic differential equations driven by Gaussian and Poisson martingale measures. It is well known that in such a setting contingent claims prices are not uniquely defined. With different criteria of chosing optimal (in some sense) equivalent martingale measures, introduced into consideration, different prices can be obtained. A more general problem consists in studying theoretically and numerically the dependence of prices on equivalent measures from some adequate classes of semimartingale probability measures. Here we present some new theoretical and numerical results obtained for the range of American options prices considered for a class of the jump-diffusion financial market models defined by stochastic differential equations driven by Wiener and Poisson processes.