On the Semimartingale Property of Discounted Asset-price Processes in Financial Modeling

A financial market model where agents trade using realistic combinations of buy-andhold strategies is considered. Minimal assumptions are made on the asset-price process — in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the “No Unbounded Profit with Bounded Risk” condition, we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures.