On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs

Julien Grépat () and Yuri Kabanov ()
Additional contact information
Julien Grépat: Université Bourgogne Franche-Comté
Yuri Kabanov: Lomonosov Moscow State University and Steklov Mathematical Institute of the Russian Academy of Sciences
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Finance and Stochastics, 2021, vol. 25, issue 1, No 7, 167-187

Abstract: Abstract We consider, using the geometric description, a sequence of models of multi-asset financial markets with proportional transaction costs vanishing in the limit. We assume that the price processes are He-type multinomial approximations of a process whose components are correlated geometric Brownian motions. For a given vector-valued contingent claim, defined as a continuous function of the price trajectories, we consider for each model the hedging set, that is, the set of all vector-valued initial endowments permitting to superreplicate the contingent claim by the final position of a self-financing portfolio. We calculate the limit of the hedging sets in the closed topology, obtaining in this way a set-valued version of the Kusuoka limit theorem.

Keywords: Hedging; Multinomial approximation; Transaction costs; Kusuoka theorem; Superreplication; 60G44 (search for similar items in EconPapers)
JEL-codes: G11 G13 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-020-00441-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:25:y:2021:i:1:d:10.1007_s00780-020-00441-4

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-020-00441-4

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().