On the optional and orthogonal decompositions of supermartingales and applications

Abdelkarem Berkaoui

Statistics & Probability Letters, 2023, vol. 199, issue C

Abstract: We consider a set Q of probability measures, which are absolutely continuous with respect to the physical probability measure P and at least one is equivalent to P. We investigate in the finite probability space case, necessary and sufficient conditions on Q, under which any Q-supermartingale can be decomposed into the sum of a Q-martingale and a decreasing process. We also provide an orthogonal decomposition of Q-super-martingales and apply this result to the orthogonal decomposition of the polar cone of Q.

Keywords: Martingale measure; m-stability; Optional decomposition; Orthogonal decomposition (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109850

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