Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints

Stochastic Processes and their Applications

Volumn 88, Issue 2, 2000, Pages 305-328

  Touzi, Nizar ^a  

^a UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

Author keywords

35K55; 49J20; 60H30; 93E20; Portfolio constraints; Primary 90A09; Secondary 60G44; Stochastic control; Stochastic volatility; Super replication problem; Viscosity solutions

Indexed keywords

EID: 0012196728     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(00)00007-7     Document Type: Article

References (18)

1. Avellaneda M., Levy A., Paras A. Pricing and hedging derivative securities in markets with uncertain volatilities. Appl. Math. Finance. 2:1995;73-88.
2. Broadie M., Cvitanić J., Soner M. Optimal replication of contingent claims under portfolio constraints. Rev. Financial Stud. 11:1996;59-78.
3. Crandall M.G., Ishii H., Lions P.L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27:1992;1-67.
4. Cvitanić J., Karatzas I. Hedging contingent claims with constrained portfolios. Ann. Appl. Probab. 3:1993;652-681.
5. Cvitanić J., Pham H., Touzi N. Super-replication in stochastic volatility models under portfolio constraints. J. Appl. Probab. 36:1999;523-525.
6. El Karoui, N., Jeanblanc-Picqué, M., Shreve, S.E., 1996. Robustness of the Black-Scholes formula. Preprint, Carnegie Mellon University.
7. El Karoui N., Quenez M.C. Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J. Control Optim. 33:1995;29-66.
8. Föllmer H., Kramkov D. Optional decomposition under constraints. Probability Theory Related Fields. 109:1997;1-25.
9. Frey, R., Sin, C.A., 1997. Bounds on European option prices under stochastic volatility. Preprint, ETH, Zurich.
10. Hull J., White A. The pricing of options on assets with stochastic volatilities. J. Finance. 42:1987;281-300.
11. Jouini E., Kallal H. Arbitrage in securities markets with short-sales constraints. Math. Finance. 3:1995;197-232.
12. Karatzas I., Shreve S.E. Brownian Motion and Stochastic Calculus. 1991;Springer, New York.
13. Krylov N.V. Controlled Diffusion Processes. 1980;Springer, New York.
14. Protter P. Stochastic Integration and Differential Equations. 1990;Springer, Berlin.
15. Rockafellar R.T. Convex Analysis. 1970;Princeton University Press, Princeton, NJ.
16. Soner, M., Touzi, N., 1998. Super-replication under Gamma constraint. SIAM J. Control Optim., to appear.
17. Soner, M., Touzi, N., 1999. Stochastic target problems dynamic programming, and viscosity solutions. Preprint.
18. Wiggins J.B. Option values under stochastic volatility: theory and empirical estimates. J. Financial Econom. 19:1987;351-372.