A nonlinear partial integro-differential equation from mathematical finance

Discrete and Continuous Dynamical Systems

Volumn 27, Issue 3, 2010, Pages 907-917

  Abergel, Frederic ^a   Tachet, Remi ^a  

^a Grande Voie des Vignes   (France)

Author keywords

Analysis of pde's; Calibration of vanillas; Fixed point methods; Local and stochastic volatility models; Nonlinear parabolic partial integro differential equation; Short time existence

Indexed keywords

EID: 77954318393     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2010.27.907     Document Type: Article

References (8)

1. F. Abergel and R. Tachet, work in progress.
2. N. Alibaud, Existence, uniqueness and regularity for nonlinear parabolic equations with non-local terms equations with nonlocal terms, NoDEA Nonlinear Differential Equations Appl., 14 (2007), 259-289.
3. H. Berestycki, J. Busca and I. Florent, Computing the implied volatility in stochastic volatility models, Comm. Pure Appl. Math., 57 (2004), 1352-1373.
4. D. Breeden and R. Litzenberger, State contingent prices implicit in option prices, Journal of Business, 51 (1978), 621-651.
5. B. Dupire, "Pricing and Hedging with Smiles," Proc AFFI Conf, La Baule, 1993.
6. A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall Inc., Englewood Cliffs, N.J., 1964.
7. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," Trans. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968.
8. A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer-Verlag, New-York, 1983.