Displaying similar documents to “A Hilbert transform for non-homogeneous martingales”

Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function

Adam Osękowski (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that 𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,..., 𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,.... The first inequality is sharp, and it is strict in all nontrivial cases.

On Existence of Local Martingale Measures for Insiders who Can Stop at Honest Times

Jakub Zwierz (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time Λ. We show, using the multiplicative decomposition of the Azéma supermartingale, that if the martingale part of the price process has the predictable representation property and Λ satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider....