Electronic Communications in Probability

Local martingales in discrete time

Vilmos Prokaj and Johannes Ruf

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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 $.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 31, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1525312855

Digital Object Identifier
doi:10.1214/18-ECP133

Mathematical Reviews number (MathSciNet)
MR3798242

Zentralblatt MATH identifier
1390.60158

Subjects
Primary: 60G42: Martingales with discrete parameter 60G48: Generalizations of martingales

Keywords
DMW theorem local and generalized martingale in discrete time

Rights
Creative Commons Attribution 4.0 International License.

Citation

Prokaj, Vilmos; Ruf, Johannes. Local martingales in discrete time. Electron. Commun. Probab. 23 (2018), paper no. 31, 11 pp. doi:10.1214/18-ECP133. https://projecteuclid.org/euclid.ecp/1525312855


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