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Finance and Stochastics

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02.12.2016

The scaling limit of superreplication prices with small transaction costs in the multivariate case

verfasst von: Peter Bank, Yan Dolinsky, Ari-Pekka Perkkiö

Erschienen in: Finance and Stochastics | Ausgabe 2/2017

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Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The \(G\)-expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.

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Our construction is motivated by the arguments we used to prove (3.2) in the previous section, which indicate which volatilities can be generated by which price systems close to \(S^{(n)}\) as in (3.1); see in particular (3.19) and compare the definition of \(A^{(n)}\) in (3.11).

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Titel: The scaling limit of superreplication prices with small transaction costs in the multivariate case
verfasst von: Peter Bank
Yan Dolinsky
Ari-Pekka Perkkiö
Publikationsdatum: 02.12.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Finance and Stochastics / Ausgabe 2/2017
Print ISSN: 0949-2984
Elektronische ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-016-0320-4

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