Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to a price interval. 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 martingale model. A result is stated for the evaluation of the price bounds by a recursive procedure.