  We consider the problem of finding model-independent bounds on the price of
an Asian option, when the call prices at the maturity date of the option are
known. Our methods differ from most approaches to model-independent pricing in
that we consider the problem as a dynamic programming problem, where the
controlled process is the conditional distribution of the asset at the maturity
date. By formulating the problem in this manner, we are able to determine the
model-independent price through a PDE formulation. Notably, this approach does
not require specific constraints on the payoff function (e.g. convexity), and
would appear to generalise to many related problems.
