Local martingales in discrete time

Abstract

For any discrete-time $P$--local martingale $S$ there exists a probability measure $Q\sim P$ such that $S$ is a $Q$--martingale. A new proof for this result is provided. The core idea relies on an appropriate modification of an argument by Chris Rogers, used to prove a version of the fundamental theorem of asset pricing in discrete time. This proof also yields that, for any $\epsilon >0$, the measure $Q$ can be chosen so that $\frac{dQ}{dP}\le 1+\epsilon$.

Accepted by Electronic Communications in Probability