Envelopes of equivalent martingale measures in an n-nomial market model

An n-nomial market model over one time period is considered, composed by a risky asset and a risk-free bond. It is well-known that such a model, though arbitrage-free, is incomplete for $n>2$, as it gives rise to a family of equivalent martingale measures. In general, given a contingent claim on the risky asset, the approach under incompleteness is to choose one of the equivalent martingale measures in the class in order to arrive at a unique no-arbitrage price for the contract. A different approach is to work with the entire class or with a suitable subclass: in this case, we get an interval of prices. Here, we provide a characterization of the lower envelope of the class of equivalent martingale measures, casting it in the Dempster-Shafer theory of evidence. We further introduce a generalized no-arbitrage principle and investigate how to obtain a pricing functional from the lower envelope which is generalized-arbitrage-free.