Abstract
For any discrete-time $\mathsf{P} $–local martingale $S$ there exists a probability measure $\mathsf{Q} \sim \mathsf{P} $ such that $S$ is a $\mathsf{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 $\varepsilon >0$, the measure $\mathsf{Q} $ can be chosen so that $\frac{\mathrm {d} \mathsf {Q}} {\mathrm{d} \mathsf{P} } \leq 1+\varepsilon $.
Citation
Vilmos Prokaj. Johannes Ruf. "Local martingales in discrete time." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP133
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