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Hedging under an expected loss constraint with small transaction costs

Bouchard, Bruno; Moreau, Ludovic; Soner, Halil Mete (2016), Hedging under an expected loss constraint with small transaction costs, SIAM Journal on Financial Mathematics, 7, 1, p. 508-551. 10.1137/15M1006787

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1309.4916v2
Date
2016
Journal name
SIAM Journal on Financial Mathematics
Volume
7
Number
1
Publisher
Society for Industrial and Applied Mathematics
Published in
Paris
Pages
508-551
Publication identifier
Metadata
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Moreau, Ludovic

Soner, Halil Mete
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.
Subjects / Keywords
Expected loss constraint; transaction cost; asymptotic expansion; hedging
JEL
D23 - Organizational Behavior; Transaction Costs; Property Rights