Before revision: We show that Lyons' rough path integral is a natural tool to use in model free financial mathematics by proving that it is possible to make an arbitrarily large profit by investing in those paths which do not have a rough path associated to them. We also show that in certain situations, the rough path integral can be constructed as a limit of Riemann sums, and not just as a limit of compensated Riemann sums which are usually used to define it.
After revision: We show that Lyons' rough path integral is a natural tool to use in model free financial mathematics by proving that it is possible to make an arbitrarily large profit by investing in those paths which do not have a rough path integral can be constructed as a limit of Riemann sums, and not just as a limit of compensated Riemann sums which are usually used to define it.