  The paper develops general, discrete, non-probabilistic market models and
minmax price bounds leading to price intervals for European options. The
approach provides the trajectory based analogue of martingale-like properties
as well as a generalization that allows a limited notion of arbitrage in the
market while still providing coherent option prices. Several properties of the
price bounds are obtained, in particular a connection with risk neutral pricing
is established for trajectory markets associated to a continuous-time
martingale model.
