Free Access
Volume 47, Number 2, March-April 2013
Page(s) 449 - 469
Published online 11 January 2013
  1. Y. Achdou and O. Pironneau, Computational Methods for Option Pricing. SIAM (2005). [Google Scholar]
  2. A. Almendral and C. Oosterlee, Numerical valuation of options with jumps in the underlying. Appl. Numer. Math. 53 (2005) 1–18. [CrossRef] [Google Scholar]
  3. L. Andersen and J. Andreasen, Jump-diffusion processes : Volatility smile fitting and numerical methods for option pricing. Rev. Deriv. Res. 4 (2000) 231–262. [CrossRef] [Google Scholar]
  4. H. Antil, M. Heinkenschloss and R. Hoppe, Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system. Optim. Methods Soft. 26 (2011) 643–669. [CrossRef] [Google Scholar]
  5. H. Antil, M. Heinkenschloss, R. Hoppe and D. Sorensen, Domain decomposition and model reduction for the numerical solution of pde constrained optimization problems with localized optimization variables. Comput. Vis. Sci. 13 (2010) 249–264. [CrossRef] [MathSciNet] [Google Scholar]
  6. N.J. Armstrong, K.J. Painter and J.A. Sherratt, A continuum approach to modelling cell-cell adhesion. J. Theor. Biol. 243 (2006) 98–113. [CrossRef] [PubMed] [Google Scholar]
  7. F. Black and M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81 (1973) 637–654. [CrossRef] [Google Scholar]
  8. R. Cont, N. Lantos and O. Pironneau, A reduced basis for option pricing. SIAM J. Financ. Math. 2 (2011) 287–316. [CrossRef] [Google Scholar]
  9. R. Cont and P. Tankov, Financial Modelling with Jump Processes, Chapman and Hall (2004). [Google Scholar]
  10. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, in Evolution Problems I 5, Springer (1992). [Google Scholar]
  11. B. Dupire, Pricing with a smile. Risk 7 (1994) 18–20. [Google Scholar]
  12. A. Gerisch, On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion. J. Numer. Anal. 30 (2010) 173–194. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Gerisch and M. Chaplain, Mathematical modelling of cancer cell invasion of tissue : Local and non-local models and the effect of adhesion. J. Theoret. Biol. 250 (2008) 684–704. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  14. M.A. Grepl and A.T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM : M2AN 39 (2005) 157–181. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  15. P. Hepperger, Option pricing in Hilbert space-valued jump-diffusion models using partial integro-differential equations. SIAM J. Financ. Math. 1 (2008) 454–489. [CrossRef] [Google Scholar]
  16. M. Hinze and S. Volkwein, Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition. Comput. Optim. Appl. 39 (2008) 319–345. [CrossRef] [MathSciNet] [Google Scholar]
  17. P. Holmes, J. Lumley and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press (1996). [Google Scholar]
  18. J.C. Hull, Options, Futures and Other Derivatives, Prentice-Hall, Upper Saddle River, N.J., 6th edition (2006). [Google Scholar]
  19. S.G. Kou, A jump-diffusion model for option pricing. Manage. Sci. 48 (2002) 1086–1101. [CrossRef] [Google Scholar]
  20. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems. Numer. Math. 90 (2001) 117–148. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.-M. Matache, T. von Petersdorff and C. Schwab, Fast deterministic pricing of options on Lévy driven assets. ESAIM : M2AN 38 (2004) 37–72. [CrossRef] [EDP Sciences] [Google Scholar]
  22. R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3 (1976) 125–144. [CrossRef] [Google Scholar]
  23. O. Pironneau, Calibration of options on a reduced basis. J. Comput. Appl. Math. 232 (2009) 139–147. [CrossRef] [Google Scholar]
  24. E.W. Sachs and M. Schu, Reduced order models (POD) for calibration problems in finance, edited by K. Kunisch, G. Of and O. Steinbach. ENUMATH 2007, Numer. Math. Adv. Appl. (2008) 735–742. [Google Scholar]
  25. E.W. Sachs and M. Schu, Reduced order models in PIDE constrained optimization. Control and Cybernetics 39 (2010) 661–675. [MathSciNet] [Google Scholar]
  26. E.W. Sachs and A. Strauss, Efficient solution of a partial integro-differential equation in finance. Appl. Numer. Math. 58 (2008) 1687–1703. [CrossRef] [Google Scholar]
  27. E.W. Sachs and S. Volkwein, POD-Galerkin approximations in PDE-constrained optimization. GAMM Reports 33 (2010) 194–208. [CrossRef] [MathSciNet] [Google Scholar]
  28. W. Schoutens, Lévy-Processes in Finance, Wiley (2003). [Google Scholar]
  29. S. Volkwein, Optimal control of a phase-field model using proper orthogonal decomposition. Z. Angew. Math. Mech. 81 (2001) 83–97. [CrossRef] [MathSciNet] [Google Scholar]
  30. S. Volkwein, Model reduction using proper orthogonal decomposition. Lecture Notes, University of Constance (2011). [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