Notes on free lunch in the limit and pricing by conjugate duality theory

King and Korf [9] introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory—it depends on the underlying probability measure more than through its null sets. However, we show that the interesting pricing results obtained by conjugate duality are still valid if it is only assumed that the market admits no free lunch rather than no free lunch in the limit.