| Abstract: | The two problems of determining the existence of arbitrage among a finite set of options and of calculating the supremum price of an option consistent with other options prices have been reduced to finding an appropriate model of bounded size in many special cases. We generalize this result to a class of arbitrage-free m -period markets with d + 1 basic securities and with no prior measure. We show there are no dominating trading strategies for a given set of l contingent claims if and only if their bid-ask prices are asymptotically consistent with models supported by at most ( l + d + 1)( d + 1) m ?1 points, if m ≥ 1 . An example showing the tightness of our bound is given. |
