Open Access
Translator Disclaimer
November 2018 Sticky processes, local and true martingales
Miklós Rásonyi, Hasanjan Sayit
Bernoulli 24(4A): 2752-2775 (November 2018). DOI: 10.3150/17-BEJ944

Abstract

We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^{p}(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close to $S$ in supremum norm. In the case where $S$ is a local martingale we may choose $Q$ arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present an application in mathematical finance.

Citation

Download Citation

Miklós Rásonyi. Hasanjan Sayit. "Sticky processes, local and true martingales." Bernoulli 24 (4A) 2752 - 2775, November 2018. https://doi.org/10.3150/17-BEJ944

Information

Received: 1 September 2015; Revised: 1 March 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853264
MathSciNet: MR3779701
Digital Object Identifier: 10.3150/17-BEJ944

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
24 PAGES


SHARE
Vol.24 • No. 4A • November 2018
Back to Top