This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group ...

The problem of valuation of American contingent claims for a jump-diffusion market model is considered. Financial assets are described by stochastic differential equations driven by Gaussian and Poisson random measures. In such setting the money market is incomplete, thus contingent claim prices are not uniquely defined. For different equivalent martingale measures different arbitrage free prices can be derived. The problem is to find exact bounds for the set of all possible prices obtained in this...