Discrete, Non Probabilistic Market Models. Arbitrage and Pricing   Intervals
  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. 
Sebastian E. Ferrando, Alfredo L. Gonzalez, Ivan L. Degano and   Massoome Rahsepar
q-fin.MF q-fin.PR