Open Access
Translator Disclaimer
2018 Local martingales in discrete time
Vilmos Prokaj, Johannes Ruf
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP133

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

Download Citation

Vilmos Prokaj. Johannes Ruf. "Local martingales in discrete time." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP133

Information

Received: 20 September 2017; Accepted: 22 April 2018; Published: 2018
First available in Project Euclid: 3 May 2018

zbMATH: 1390.60158
MathSciNet: MR3798242
Digital Object Identifier: 10.1214/18-ECP133

Subjects:
Primary: 60G42 , 60G48

Keywords: DMW theorem , local and generalized martingale in discrete time

JOURNAL ARTICLE
11 PAGES


SHARE
Back to Top