On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs
type: Item
instance of: scholarly article
title: On a multi-asset version of the Kusuoka limit theorem of option superreplication under transaction costs
zbMATH Open document ID: 1471.91569
author: Julien Grépat
author: Yuri Kabanov
published in: Finance and Stochastics
publication date: 2021-04-29T00:00:00Z
review text: In this technical paper, the authors show how to avoid the typical monetary context for pricing financial derivatives. They point out how conventional attempts to include ideas such as transaction costs are challenging. Within this context, elementary economic considerations can prove helpful. By using solvency cones the authors include transaction costs as constraints on investors' choice. Although these concepts are of a polyhedral type, the paper considers a more general setting of conic contracts, which cover the modelling of financial products. A geometric perspective sits at the heart of this approach. This study is in the context of no-arbitrage criteria and hedging techniques. This allows for a natural slant to set model sensitivities in a set-valued framework. This allows the inclusion of transaction costs vanishing in the limit. The authors substantiate the convergence of hedging sets in the closed topology. This leads to a set-valued version of the Kusuoka theorem. The core result presents the convergence of a series of measures. This leads to a result on the closed convergence of hedging sets to an affine half-space. The work concludes with several technical results pertaining to scaler discrete-time martingale.
reviewed by: John O'Hara
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 7341435
zbMATH Keywords: hedging
zbMATH Keywords: multinomial approximation
zbMATH Keywords: transaction costs
zbMATH Keywords: Kusuoka theorem
zbMATH Keywords: superreplication
MaRDI profile type: Publication
full work available at URL: s00780-020-00441-4
OpenAlex ID: W3113831621
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DOI: 10.1007/S00780-020-00441-4
description: scientific article; zbMATH DE number 7341435