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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

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

Suggested Citation

  • Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, vol. 17(1), pages 31-72, January.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:31-72
    DOI: 10.1007/s00780-012-0198-8
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    References listed on IDEAS

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    1. repec:hal:wpaper:hal-00422427 is not listed on IDEAS
    2. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    3. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    4. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    5. repec:dau:papers:123456789/1533 is not listed on IDEAS
    6. 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.
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    Cited by:

    1. Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Mohan Yang, 2023. "An optimal transport approach for the multiple quantile hedging problem," Papers 2308.01121, arXiv.org.
    2. Olivier Gu'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832, arXiv.org, revised May 2014.
    3. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    4. Remi Genet, 2025. "Deep Learning for VWAP Execution in Crypto Markets: Beyond the Volume Curve," Papers 2502.13722, arXiv.org, revised Apr 2025.
    5. Olivier Guéant & Royer Guillaume, 2014. "VWAP execution and guaranteed VWAP," Post-Print hal-01393121, HAL.
    6. Francesco Cordoni & Luca Di Persio & Luca Prezioso, 2019. "A lending scheme for a system of interconnected banks with probabilistic constraints of failure," Papers 1903.06042, arXiv.org, revised Oct 2019.
    7. Bayraktar, Erhan & Yao, Song, 2024. "Stochastic control/stopping problem with expectation constraints," Stochastic Processes and their Applications, Elsevier, vol. 176(C).

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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