On the martingale property of economic and financial instruments

The solutions to many economic and financial instruments are stochastic processes that are required to be arbitrage-free or martingale under an equivalent probability measure known as martingale measure. The main vehicle to verify the existence of an equivalent martingale measure is the Girsanov theorem. This study shows that some of the usual assumptions regarding the underlying stochastic base often employed in applied literature could nullify the theorem and its applications. Further, it is shown that the infinite-horizon Girsanov setting may not contain an equivalent martingale measure.