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A. Cox, S. Källblad:
"Model-Independent Bounds for Asian Options: A Dynamic Programming Approach";
SIAM Journal on Control and Optimization, Volume 55 (2017), Issue 6; 3409 - 3436.

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 generalize to many related problems.
Read More: http://epubs.siam.org/doi/abs/10.1137/16M1087527

model-independent pricing dynamic programming measure-valued martingale / subject classifications: 91G20, 93E20, 49L20, 60G48;

http://dx.doi.org/10.1137/16M1087527

http://epubs.siam.org/doi/abs/10.1137/16M1087527