  The paper studies sub and super-replication price bounds for contingent
claims defined on general trajectory based market models. No prior
probabilistic or topological assumptions are placed on the trajectory space,
trading is assumed to take place at a finite number of occasions but not
bounded in number nor necessarily equally spaced in time. For a given option,
there exists an interval bounding the set of possible fair prices; such
interval exists under more general conditions than the usual no-arbitrage
requirement. The paper develops a backward recursive method to evaluate the
option bounds; the global minmax optimization, defining the price interval, is
reduced to a local minmax optimization via dynamic programming. Trajectory sets
are introduced for which existing non-probabilistic markets models are nested
as a particular case. Several examples are presented, the effect of the
presence of arbitrage on the price bounds is illustrated.
