A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 23, Issue 5, 2006, Pages 695-711

  Arisawa, Mariko ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Existence and uniqueness results; Integro differential equations; L vy operator; Viscosity solutions

Indexed keywords

BOUNDARY CONDITIONS; BROWNIAN MOVEMENT; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; VISCOSITY;

DIRICHLET BOUNDARY CONDITION; LÉVY OPERATOR; NEUMANN BOUNDARY CONDITION; VISCOSITY SOLUTIONS;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 33748687967     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2005.09.002     Document Type: Article

References (17)

1. Y. Achdou, O. Pironneau, Computational methods for option pricing, in preparation
2. Alvarez O., and Tourin A. Viscosity solutions of nonlinear integro-differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 13 3 (1996) 293-317
3. Arisawa M. Some ergodic problems for Hamilton-Jacobi equations in Hilbert space. Differential Integral Equations 9 1 (1996) 59-70
4. M. Arisawa, Ergodic problems for a class of integro-differential equations, in preparation
5. Barles G., Buckdahn R., and Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stochastics Stochastics Rep. 60 1-2 (1997) 57-83
6. Bensoussan A., and Lions J.L. Impulse Control and Quasi-Variational Inequalities (1984), Gauthier-Villars, Paris
7. Cont R., and Tankov P. Financial Modelling with Jump Processes (2004), Chapman and Hall/CRC
8. Crandall M.G., Ishii H., and Lions P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 1 (1992)
9. Framstad N.C., Oksendal B., and Sulem A. Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs. J. Math. Econom. 35 2 (2001) 233-257
10. Garroni M.G., and Menaldi J.L. Second-Order Elliptic Integro-Differential Problems. Res. Notes Math. vol. 430 (2002), Chapmam and Hall/CRC
11. Gimbert F., and Lions P.-L. Existence and regularity results for solutions of second-order elliptic integro-differential operators. Ricerche Mat. 33 2 (1984) 315-358
12. C. Imbert, A non-local regularization of first order Hamilton-Jacobi equations, J. Differential Equations, in press
13. E.R. Jacobsen, K.H. Karlsen, A maximum principle for semicontinuous functions applications to integro-partial differential equations, Dept. of Math. Univ. of Oslo Pure Maths, no. 18, 2003
14. Miyahara Y. Minimal entropy martingale measure of jump type price processes in incomplete assets markets. Asia-Pacific Financial Markets 6 (1999) 97-113
15. Pham H. Optimal stopping of controlled jump diffusion processes; A viscosity solution approach. J. Math. Systems Estim. Control 8 1 (1998)
16. Sato K.-I. Lévy Processes and Infinitely Divisible Distributions (1999), Cambridge University Press, Cambridge, UK
17. Sayah A. Equations d'Hamilton-Jacobi du premiere ordre avec termes integro-differentielles: parties 1 et 2. Comm. Partial Differential Equations 16 (1991) 1053-1093