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Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation

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Date
2013
Dewey
Probabilités et mathématiques appliquées
Sujet
Stochastic target problems; State constraints; Pricing under risk constraint; Book liquidation
Journal issue
Finance and Stochastics
Volume
17
Number
1
Publication date
2013
Article pages
31-72
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00780-012-0198-8
URI
https://basepub.dauphine.fr/handle/123456789/4696
Collections
  • CEREMADE : Publications
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Author
Bouchard, Bruno
Dang, Ngoc Minh
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a singular with state constraints version of the stochastic target problems studied in Soner and Touzi (2002) and more recently Bouchard, Elie and Touzi (2008), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly suits to market models with proportional transaction costs and to order book liquidation issues. Our main result is a PDE characterization of the associated pricing function. As an example of application, we discuss the evaluation of VWAP-guaranteed type book liquidation contracts, for a general class of risk functions.

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