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Hedging under an expected loss constraint with small transaction costs

Bruno Bouchard (bouchard@ceremade.dauphine.fr), Ludovic Moreau (ludovic.moreau@univ-grenoble-alpes.fr) and Mete Soner (hmsoner@ethz.ch)
Additional contact information
Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique
Ludovic Moreau: D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]
Mete Soner: D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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Abstract: 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.

Keywords: asymptotic expansion; Expected loss constraint; hedging; transaction cost; asymptotic expansion. (search for similar items in EconPapers)
Date: 2016-06-01
New Economics Papers: this item is included in nep-rmg and nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-00863562v2
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Citations: View citations in EconPapers (7)

Published in SIAM Journal on Financial Mathematics, 2016, 7 (1), pp.508-551

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