Trajectorial market models: Arbitrage and pricing intervals

The paper develops general, non-probabilistic market models based on trajectory sets and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of a martingale process as well as a generalization that allows a limited notion of arbitrage in the market while still providing coherent option prices. An illustrative example is described in detail. 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.Fil: Ferrando, Sebastian Esteban. Ryerson University; CanadáFil: González, Alfredo Lázaro. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Degano, Iván Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Rahsepar, Massoomeh. Ryerson University; Canad