Free Access
Issue
ESAIM: M2AN
Volume 38, Number 2, March-April 2004
Page(s) 359 - 369
DOI https://doi.org/10.1051/m2an:2004018
Published online 15 March 2004
  1. G. Barles and B. Perthame, Discontinuous solutions of deterministic optimal stopping time problems. RAIRO Modél. Math. Anal. Numér. 21 (1987) 557–579. [MathSciNet] [Google Scholar]
  2. G. Barles and B. Perthame, Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26 (1988) 1133–1148. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Barles and H.M. Soner, Option pricing with transaction costs and a nonlinear Black-Scholes equation. Finance Stoch. 2 (1998) 369–397. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Barles and P.E. Souganides, Convergence of approximation schemes for fully nonlinear second order equations. Asympt. Anal. 4 (1991) 271–283. [Google Scholar]
  5. G. Barles, Ch. Daher and M. Romano, Convergence of numerical schemes for parabolic equations arising in finance theory. Math. Models Meth. Appl. Sci. 5 (1995) 125–143. [CrossRef] [Google Scholar]
  6. F. Black and M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81 (1973) 637–659. [CrossRef] [Google Scholar]
  7. R. Bodenmann and H.J. Schroll, Compact difference methods applied to initial-boundary value problems for mixed systems. Numer. Math. 73 (1996) 291–309. [CrossRef] [MathSciNet] [Google Scholar]
  8. P. Boyle and T. Vorst, Option replication in discrete time with transaction costs. J. Finance 47 (1973) 271–293. [CrossRef] [Google Scholar]
  9. G.M. Constantinides and T. Zariphopoulou, Bounds on process of contingent claims in an intertemporal economy with proportional transaction costs and general preferences. Finance Stoch. 3 (1999) 345–369. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Davis, V. Panis and T. Zariphopoulou, European option pricing with transaction fees. SIAM J. Control Optim. 31 (1993) 470–493. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. Düring, M. Fournié and A. Jüngel, High order compact finite difference schemes for a nonlinear Black-Scholes equation. Int. J. Appl. Theor. Finance 6 (2003) 767–789. [CrossRef] [Google Scholar]
  14. R. Frey, Perfect option hedging for a large trader. Finance Stoch. 2 (1998) 115–141. [CrossRef] [Google Scholar]
  15. R. Frey, Market illiquidity as a source of model risk in dynamic hedging, in Model Risk, R. Gibson Ed., RISK Publications, London (2000). [Google Scholar]
  16. G. Genotte and H. Leland, Market liquidity, hedging and crashes. Amer. Econ. Rev. 80 (1990) 999–1021. [Google Scholar]
  17. S.D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs. Rev. Future Markets 8 (1989) 222–239. [Google Scholar]
  18. V.P. Il'in, On high-order compact difference schemes. Russ. J. Numer. Anal. Math. Model. 15 (2000) 29–46. [CrossRef] [Google Scholar]
  19. H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Ann. Scuola Norm. Sup. Pisa 16 (1989) 105–135. [Google Scholar]
  20. R. Jarrow, Market manipulation, bubbles, corners and short squeezes. J. Financial Quant. Anal. 27 (1992) 311–336. [CrossRef] [Google Scholar]
  21. P. Kangro and R. Nicolaides, Far field boundary conditions for Black-Scholes equations. SIAM J. Numer. Anal. 38 (2000) 1357–1368. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliqué à la finance. 2e édn., Ellipses, Paris (1997). [Google Scholar]
  23. J. Leitner, Continuous time CAPM, price for risk and utility maximization, in Mathematical Finance. Workshop of the Mathematical Finance Research Project, Konstanz, Germany, M. Kohlmann et al. Eds., Birkhäuser, Basel (2001). [Google Scholar]
  24. R.C. Merton, Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4 (1973) 141–183. [CrossRef] [Google Scholar]
  25. D. Michelson, Convergence theorem for difference approximations of hyperbolic quasi-linear initial-boundary value problems. Math. Comput. 49 (1987) 445–459. [Google Scholar]
  26. E. Platen and M. Schweizer, On feedback effects from hedging derivatives. Math. Finance 8 (1998) 67–84. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Rigal, High order difference schemes for unsteady one-dimensional diffusion-convection problems. J. Comp. Phys. 114 (1994) 59–76. [CrossRef] [Google Scholar]
  28. P. Schönbucher and P. Wilmott, The feedback effect of hedging in illiquid markets. SIAM J. Appl. Math. 61 (2000) 232–272. [CrossRef] [MathSciNet] [Google Scholar]
  29. H.M. Soner, S.E. Shreve and J. Cvitanic, There is no nontrivial hedging portfolio for option pricing with transaction costs. Ann. Appl. Probab. 5 (1995) 327–355. [CrossRef] [MathSciNet] [Google Scholar]
  30. G. Strang, Accurate partial difference methods. II: Non-linear problems. Numer. Math. 6 (1964) 37–46. [CrossRef] [MathSciNet] [Google Scholar]
  31. C. Wang and J. Liu, Fourth order convergence of compact finite difference solver for 2D incompressible flow. Commun. Appl. Anal. 7 (2003) 171–191. [MathSciNet] [Google Scholar]
  32. A. Whalley and P. Wilmott, An asymptotic analysis of an optimal hedging model for option pricing with transaction costs. Math. Finance 7 (1997) 307–324. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you