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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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  • Bruno Bouchard

    ()

  • Ngoc-Minh Dang

    ()

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    Abstract

    We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404–424, 2002 ; J. Eur. Math. Soc. 4:201–236, 2002 ) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123–3150, 2009 ), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly fits the market models with proportional transaction costs and the order book liquidation issues. Our main result is a direct PDE characterization of the associated pricing function. As an example application, we discuss the valuation of VWAP-guaranteed-type book liquidation contracts, for a general class of risk functions. Copyright Springer-Verlag 2013

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    File URL: http://hdl.handle.net/10.1007/s00780-012-0198-8
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 17 (2013)
    Issue (Month): 1 (January)
    Pages: 31-72

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    Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:31-72

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    Related research

    Keywords: Stochastic target problems; State constraints; Pricing under risk constraint; Book liquidation; 49L25; 60J60; 91G80; G11; G13; C61;

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    1. Touzi, Nizar, 2000. "Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 305-328, August.
    2. Bouchard, Bruno & Touzi, Nizar, 2000. "Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs," Economics Papers from University Paris Dauphine 123456789/1533, Paris Dauphine University.
    3. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    4. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
    5. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    6. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
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