Résumé en anglais

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.