The multi-dimensional super-replication problem under gamma constraints
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 5, pp. 633-666. 
@article{AIHPC_2005__22_5_633_0,
     author = {Cheridito, Patrick and Soner, H. Mete and Touzi, Nizar},
     title = {The multi-dimensional super-replication problem under gamma constraints},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {633--666},
     publisher = {Elsevier},
     volume = {22},
     number = {5},
     year = {2005},
     doi = {10.1016/j.anihpc.2004.10.012},
     mrnumber = {2171995},
     zbl = {1078.91010},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.012/}
}
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Cheridito, Patrick; Soner, H. Mete; Touzi, Nizar. The multi-dimensional super-replication problem under gamma constraints. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 5, pp. 633-666. doi : 10.1016/j.anihpc.2004.10.012. http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.012/

[1] Bank P., Baum D., Hedging and portfolio optimization in financial markets with a large trader, Math. Finance 14 (1) (2004) 1-18. | MR | Zbl

[2] Barles G., Solutions de Viscosité des Equations de Hamilton-Jacobi, Math. Appl., vol. 17, Springer-Verlag, Paris, 1994. | MR | Zbl

[3] Broadie M., Cvitanić J., Soner H.M., Optimal replication of contingent claims under portfolio constraints, Rev. Financial Stud. 11 (1998) 59-79.

[4] P. Cheridito, H.M. Soner, N. Touzi, Small time path behavior of double stochastic integrals and applications to stochastic control, Preprint, 2003. | MR

[5] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1) (1992) 1-67. | MR | Zbl

[6] Cvitanić J., Karatzas I., Hedging contingent claims with constrained portfolios, Ann. Appl. Probab. 3 (3) (1993) 652-681. | MR | Zbl

[7] Cvitanić J., Pham H., Touzi N., Super-replication in stochastic volatility models under portfolio constraints, J. Appl. Probab. 36 (2) (1999) 523-545. | MR | Zbl

[8] Fleming W.H., Soner H.M., Controlled Markov Processes and Viscosity Solutions, Math. Appl., vol. 25, Springer-Verlag, New York, 1993. | MR | Zbl

[9] Föllmer H., Kramkov D., Optional decomposition under constraints, Probab. Theory Related Fields 109 (1) (1997) 1-25. | MR | Zbl

[10] Jouini E., Kallal H., Arbitrage in securities markets with short-sales constraints, Math. Finance 5 (3) (1995) 197-232. | MR | Zbl

[11] Karatzas I., Shreve S., Methods of Mathematical Finance, Math. Appl., vol. 39, Springer-Verlag, New York, 1998. | MR | Zbl

[12] Kurtz T.G., Protter P., Weak convergence of stochastic integrals and differential equations, in: Talay D., Tubaro L. (Eds.), Probabilistic Models for Nonlinear Partial Differential Equations, Montecatini Terme, 1995, Lecture Notes in Math., vol. 1629, 1996, pp. 1-41. | MR | Zbl

[13] Levental S., Skorohod A.V., On the possibility of hedging options in the presence of transaction costs, Ann. Appl. Probab. 7 (2) (1997) 410-443. | MR | Zbl

[14] Revuz D., Yor M., Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999. | MR | Zbl

[15] Soner H.M., Touzi N., Super-replication under gamma constraints, SIAM J. Control Optim. 39 (1) (2000) 73-96. | Zbl

[16] Soner H.M., Touzi N., Stochastis target problem, dynamic programming, and viscosity solutions, SIAM J. Control Optim. 41 (2) (2002) 404-424. | MR | Zbl

[17] Soner H.M., Touzi N., Dynamic programming for stochastic target problems and geometric flows, J. Eur. Math. Soc. 4 (3) (2002) 201-236. | MR | Zbl

[18] Touzi N., Direct characterization of the value of super-replication under stochastic volatility and portfolio constraint, Stochastic Process. Appl. 88 (2) (2000) 305-328. | MR | Zbl

[19] Touzi N., Stochastic Control and Application to Finance, Lecture Notes, Scuola Normale Superiore Pisa, 2002. | Zbl

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