Model Choice and Arbitrage

Seeking a vantage point suitable for model choice, we recast three different degrees of absence of arbitrage into a unified multidimensional semimartingale setting: absence of arbitrage of the first kind for the large set of allowable strategies, for the medium set of admissible strategies, and for the smaller set of simple no short sales trading. Each of these degrees of absence of arbitrage is equivalent to the existence of a type of equivalent deflator: martingale, local martingale, and supermartingale deflator. Comparing these results highlights their beautiful symmetry, shows which types of strategies may create arbitrage in which kind of models, and reveals settings that level the differences between two or three of the different degrees of absence of arbitrage. Understanding these phenomena and the resulting model risk can be useful when choosing between models for a specific purpose.