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

Article English OPEN
Bouchard , Bruno; Dang , Ngoc Minh;
(2013)
  • Publisher: Springer Verlag (Germany)
  • Subject: [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR] | 49L25, 60J60; 49L20, 35K55 | Book liquidation | [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] | Stochastic target problems | State constraints | Pricing under risk constraint | Book liquidation.

International audience; 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 contin... View more
  • References (13)
    13 references, page 1 of 2

    [1] B. Bouchard, R. Elie, and N. Touzi. Stochastic target problems with controlled loss. SIAM Journal on Control and Optimization, 48(5), 3123-3150, 2009.

    [2] B. Bouchard and N. Touzi. Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs, Annals of Applied Probability, 10, 685-708, 2000.

    [3] B. Bouchard and T. N. Vu. The American version of the geometric dynamic programming principle, Application to the pricing of american options under constraints. Applied Mathematics and Optimization, 61(2), 235-265, 2010.

    [4] P. Cheridito, M. Soner and N. Touzi, The multi-dimensional super-replication problem under Gamma constraints. Annales de l'Institut Henri Poincar´e, S´erie C: Analyse NonLin´eaire 22, 633-666, 2005.

    [5] M. Crandall, H. Ishii, and P.-L. Lions. User's guide to viscosity solutions of second order partial differential equations. American Mathematical Society, 27, 1-67, 1992.

    [6] J. Cvitani´c, H. Pham and N. Touzi. A closed-form solution to the problem of superreplication under transaction costs. Finance and Stochastics, 3, 35-54, 1999.

    [7] J. Cvitani´c, H. Pham and N. Touzi. Super-replication in stochastic volatility models with portfolio constraints. Journal of Applied Probability, 36, 523-545, 1999.

    [8] P. Dupuis and H. Ishii. SDEs with oblique reflection on nonsmooth domains. The Annals of Probability, 21(1), 554-580, 1993.

    [9] H. Fo¨llmer and P. Leukert. Quantile Hedging. Finance and Stochastics, 3(3), 251-273, 1999.

    [10] H. Fo¨llmer and P. Leukert. Efficient hedging : cost versus shortfall risk. Finance and Stochastics, 4, 117-146, 2000.

  • Metrics
Share - Bookmark