Barrier option hedging under constraints: A viscosity approach

SIAM Journal on Control and Optimization

Volumn 45, Issue 5, 2006, Pages 1846-1874

  Bentahart, Imen ^a   Bouchard, Bruno ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Barrier options; Portfolio constraints; Superreplication; Viscosity solutions

Indexed keywords

BROWNIAN MOVEMENT; COMPUTER SIMULATION; PROBLEM SOLVING; VECTORS; VISCOSITY MEASUREMENT;

BARRIER OPTIONS; BROWNIAN DIFFUSION; PORTFOLIO CONSTRAINTS; SUPERREPLICATION; VISCOSITY SOLUTIONS;

CONSTRAINT THEORY;

EID: 34648830400     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/06065324X     Document Type: Article

References (17)

1. G. BARLES AND P. E. SOUGANIDIS, Convergence of approximation schemes for fully nonlinear second order equations, Asymptot. Anal., 4 (1991), pp. 271-283.
2. I. BENTAHAR, Numerical resolution of the barrier option pricing problem under constraints, forthcoming.
3. B. BOUCHARD, Stochastic targets with mixed diffusion processes, Stochastic Process. Appl., 101 (2002), pp. 273-302.
4. M. BROADIE, J. CVITANIC̀, AND M. SONER, Optimal replication of contingent claims under portfolio constraints, Rev. Financial Stud., 11 (1998), pp. 59-79.
5. M. G. CRANDALL, H. ISHII, AND P.-L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Amer. Math. Soc., 27 (1992), pp. 1-67.
6. J. CVITANIC̀ AND I. KARATZAS, Hedging contingent claims with constrained portfolios, Ann. Appl. Probab., 3 (1993), pp. 652-681.
7. J. CVITANIC̀, H. PHAM, AND N. TOUZI, Super-replication in stochastic volatility models with portfolio constraints, J. Appl. Probab., 36 (1999), pp. 523-545.
8. H. FÖLLMER AND D. KRAMKOV, Optional decomposition under constraints, Probab. Theory Related Fields, 109 (1997), pp. 1-25.
9. D. GILBARG AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977.
10. I. KARATZAS AND S. E. SHREVE, Methods of Mathematical Finance, Springer-Verlag, New York, 1998.
11. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
12. S. E. SHREVE, U. SCHMOCK, AND U. WYSTUP, Valuation of exotic options under shortselling constraints, Finance Stoch., 6 (2002), pp. 143-172.
13. S. E. SHREVE, U. SCHMOCK, AND U. WYSTUP, Dealing with dangerous digitals, in Foreign Exchange Risk, Risk Publications, London, 2002, pp. 327-348.
14. H. M. SONER AND N. TOUZI, Dynamic programming for stochastic target problems and geometric flows, J. Eur. Math. Soc. (JEMS), 4 (2002), pp. 201-236.
15. H. M. SONER AND N. TOUZI, Stochastic target problems, dynamic programming, and viscosity solutions, SIAM J. Control Optim., 41 (2002), pp. 404-424.
16. H. M. SONER AND N. TOUZI The problem of super-replication under constraints, in Paris-Princeton Lectures on Mathematical Finance, Lecture Notes in Math. 1814, Springer-Verlag, Berlin, 2004, pp. 133-172.
17. N. TOUZI, Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints, Stochastic Process. Appl., 88 (2000), pp. 305-328.