Volume 47, Number 2, March-April 2013
|Page(s)||449 - 469|
|Published online||11 January 2013|
- Y. Achdou and O. Pironneau, Computational Methods for Option Pricing. SIAM (2005).
- A. Almendral and C. Oosterlee, Numerical valuation of options with jumps in the underlying. Appl. Numer. Math. 53 (2005) 1–18. [CrossRef]
- 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]
- 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]
- 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]
- 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]
- F. Black and M. Scholes, The pricing of options and corporate liabilities. J. Polit. Econ. 81 (1973) 637–654. [CrossRef]
- R. Cont, N. Lantos and O. Pironneau, A reduced basis for option pricing. SIAM J. Financ. Math. 2 (2011) 287–316. [CrossRef]
- R. Cont and P. Tankov, Financial Modelling with Jump Processes, Chapman and Hall (2004).
- R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, in Evolution Problems I 5, Springer (1992).
- B. Dupire, Pricing with a smile. Risk 7 (1994) 18–20.
- 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]
- 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]
- 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]
- 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]
- 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]
- P. Holmes, J. Lumley and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press (1996).
- J.C. Hull, Options, Futures and Other Derivatives, Prentice-Hall, Upper Saddle River, N.J., 6th edition (2006).
- S.G. Kou, A jump-diffusion model for option pricing. Manage. Sci. 48 (2002) 1086–1101. [CrossRef]
- K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems. Numer. Math. 90 (2001) 117–148. [CrossRef] [MathSciNet]
- 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]
- R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3 (1976) 125–144. [CrossRef]
- O. Pironneau, Calibration of options on a reduced basis. J. Comput. Appl. Math. 232 (2009) 139–147. [CrossRef]
- 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.
- E.W. Sachs and M. Schu, Reduced order models in PIDE constrained optimization. Control and Cybernetics 39 (2010) 661–675. [MathSciNet]
- E.W. Sachs and A. Strauss, Efficient solution of a partial integro-differential equation in finance. Appl. Numer. Math. 58 (2008) 1687–1703. [CrossRef]
- E.W. Sachs and S. Volkwein, POD-Galerkin approximations in PDE-constrained optimization. GAMM Reports 33 (2010) 194–208. [CrossRef] [MathSciNet]
- W. Schoutens, Lévy-Processes in Finance, Wiley (2003).
- S. Volkwein, Optimal control of a phase-field model using proper orthogonal decomposition. Z. Angew. Math. Mech. 81 (2001) 83–97. [CrossRef] [MathSciNet]
- S. Volkwein, Model reduction using proper orthogonal decomposition. Lecture Notes, University of Constance (2011).
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