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In this paper we establish an arbitrage-free prices interval for American contingent claims in incomplete financial markets. Such an incom- pleteness derives from considering uncertain volatility. We use the notion of G-expectation, under which the corresponding canonical path is a G-Brownian Motion, and the related Ito stochastic calculus on suitable stopping time inter- vals, in a standard financial market characterized by a risk-less asset and one risky stock.

AN INTERVAL OF NO-ARBITRAGE PRICES FOR AMERICAN CONTINGENT CLAIMS IN INCOMPLETE MARKETS