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Hedging under an expected loss constraint with small transaction costs

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Date
2016
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1309.4916v2
Dewey
Probabilités et mathématiques appliquées
Sujet
Expected loss constraint; transaction cost; asymptotic expansion; hedging
JEL code
D23
Journal issue
SIAM Journal on Financial Mathematics
Volume
7
Number
1
Publication date
2016
Article pages
508-551
Publisher
Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/15M1006787
URI
https://basepub.dauphine.fr/handle/123456789/11907
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Bouchard, Bruno
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Moreau, Ludovic
Soner, Halil Mete
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are also obtained in the special cases of an exponential or power loss function. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

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