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

Bouchard, Bruno; Dang, Ngoc Minh

Bouchard, Bruno; Dang, Ngoc Minh (2013), Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation, Finance and Stochastics, 17, 1, p. 31-72. http://dx.doi.org/10.1007/s00780-012-0198-8

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Type

Article accepté pour publication ou publié

Date

2013

Journal name

Finance and Stochastics

Volume

Number

Publisher

Springer

Pages

31-72

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.

Subjects / Keywords

Stochastic target problems; State constraints; Pricing under risk constraint; Book liquidation