Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation
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
Volume (Year): 17 (2013)
Issue (Month): 1 (January)
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References listed on IDEAS
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- Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag\`es, 2009.
"Optimal split of orders across liquidity pools: a stochastic algorithm approach,"
0910.1166, arXiv.org, revised May 2010.
- Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2010. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
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- repec:dau:papers:123456789/1533 is not listed on IDEAS
- 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. Full references (including those not matched with items on IDEAS)
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