On the support of extremal martingale measures with given marginals: the countable case

Campi, Luciano and Martini, Claude (2019) On the support of extremal martingale measures with given marginals: the countable case. Advances in Applied Probability, 51 (2). pp. 570-605. ISSN 0001-8678

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Abstract

We investigate the supports of extremal martingale measures with prespecified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure Q and the denseness in of a suitable linear subspace, which can be seen in a financial context as the set of all semistatic trading strategies. Moreover, when the supports of both marginals are countable, we focus on the slightly stronger notion of weak exact predictable representation property (WEP) and provide two combinatorial sufficient conditions, called the '2-link property' and 'full erasability', on how the points in the supports are linked to each other for granting extremality. When the support of the first marginal is a finite set, we give a necessary and sufficient condition for the WEP to hold in terms of the new concepts of 2-net and deadlock. Finally, we study the relation between cycles and extremality.

Item Type:	Article
Additional Information:	© 2019 Applied Probability Trust
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	08 Mar 2019 10:00
Last Modified:	20 Sep 2024 02:00
URI:	http://eprints.lse.ac.uk/id/eprint/100225

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