The Second Fundamental Theorem of Asset Pricing: A New Approach

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Abstract
This article presents a new definition of market completeness that is independent of the notions of no arbitrage and equivalent martingale measures. Our definition has many advantages, all shown herein. First, it preserves the Second Fundamental Theorem of Asset Pricing, even in complex economies. Second, under our definition, the market can be complete yet arbitrage opportunities exist. This is important in practice, and stands in contrast to the traditional definitions. Third, under the assumptions of no arbitrage and when used in the standard models, our definition is equivalent to the traditional one.