Sticky processes, local and true martingales

Miklós Rásonyi; Hasanjan Sayit

doi:10.3150/17-BEJ944

Sticky processes, local and true martingales

Miklós Rásonyi^*, Hasanjan Sayit

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S that is arbitrarily close to S in L^p(Q) norm. For continuous S, 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.

Original language	English
Pages (from-to)	2429-2460
Number of pages	32
Journal	Bernoulli
Volume	24
Issue number	4A
DOIs	https://doi.org/10.3150/17-BEJ944
Publication status	Published - Nov 2018
Externally published	Yes

Keywords

Consistent price systems
Illiquid markets
Martingales
Processes with jumps
Sticky processes

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10.3150/17-BEJ944

Cite this

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title = "Sticky processes, local and true martingales",

abstract = "We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S that is arbitrarily close to S in Lp(Q) norm. For continuous S, 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.",

keywords = "Consistent price systems, Illiquid markets, Martingales, Processes with jumps, Sticky processes",

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AU - Sayit, Hasanjan

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N2 - We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S that is arbitrarily close to S in Lp(Q) norm. For continuous S, 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.

AB - We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S that is arbitrarily close to S in Lp(Q) norm. For continuous S, 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.

KW - Consistent price systems

KW - Illiquid markets

KW - Martingales

KW - Processes with jumps

KW - Sticky processes

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DO - 10.3150/17-BEJ944

M3 - Article

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VL - 24

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JO - Bernoulli

JF - Bernoulli

IS - 4A

ER -

Sticky processes, local and true martingales

Abstract

Keywords

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