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Mat. Zametki, 2007, Volume 81, Issue 4, Pages 614–620 (Mi mz3703)  

This article is cited in 3 scientific papers (total in 3 papers)

A Theorem on Martingale Selection for Relatively Open Convex Set-Valued Random Sequences

D. B. Rokhlin

Rostov State University

Abstract: For set-valued random sequences $(G_n)_{n=0}^N$ with relatively open convex values $G_n(\omega)$, we prove a new test for the existence of a sequence $(x_n)_{n=0}^N$ of selectors adapted to the filtration and admitting an equivalent martingale measure. The statement is formulated in terms of the supports of regular upper conditional distributions of $G_n$. This is a strengthening of the main result proved in our previous paper [1], where the openness of the set $G_n(\omega)$ was assumed and a possible weakening of this condition was discussed.

Keywords: representation, set-valued random sequence, martingale selection, measurable set-valued map, arbitrage theory, market model, pricing process

DOI: https://doi.org/10.4213/mzm3703

Full text: PDF file (451 kB)
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English version:
Mathematical Notes, 2007, 81:4, 543–548

Bibliographic databases:

UDC: 519.216.8
Received: 28.02.2006

Citation: D. B. Rokhlin, “A Theorem on Martingale Selection for Relatively Open Convex Set-Valued Random Sequences”, Mat. Zametki, 81:4 (2007), 614–620; Math. Notes, 81:4 (2007), 543–548

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. B. Rokhlin, “Recurrence relations for price bounds of contingent claims in discrete time market models”, Theory Probab. Appl., 56:1 (2012), 72–95  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Denis E., Kabanov Yu., “Consistent price systems and arbitrage opportunities of the second kind in models with transaction costs”, Finance Stoch., 16:1 (2012), 135–154  crossref  mathscinet  zmath  isi  elib  scopus
    3. Sass J., Smaga M., “Ftap in Finite Discrete Time With Transaction Costs By Utility Maximization”, Financ. Stoch., 18:4 (2014), 805–823  crossref  mathscinet  zmath  isi  scopus
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