  The paper develops no arbitrage results for trajectory based models by
imposing general constraints on the trading portfolios. The main condition
imposed, in order to avoid arbitrage opportunities, is a local continuity
requirement on the final portfolio value considered as a functional on the
trajectory space. The paper shows this to be a natural requirement by proving
that a large class of practical trading strategies, defined by means of
trajectory based stopping times, give rise to locally continuous functionals.
The theory is illustrated, with some detail, for two specific trajectory models
of practical interest. The implications for stochastic models which are not
semimartingales are described. The present paper extends some of the results in
[1] by incorporating in the formalism a larger set of trading portfolios.

Probability;General Finance