• Bernoulli
  • Volume 24, Number 4A (2018), 2752-2775.

Sticky processes, local and true martingales

Miklós Rásonyi and Hasanjan Sayit

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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.

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Bernoulli, Volume 24, Number 4A (2018), 2752-2775.

Received: September 2015
Revised: March 2017
First available in Project Euclid: 26 March 2018

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consistent price systems illiquid markets martingales processes with jumps sticky processes


Rásonyi, Miklós; Sayit, Hasanjan. Sticky processes, local and true martingales. Bernoulli 24 (2018), no. 4A, 2752--2775. doi:10.3150/17-BEJ944.

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