no. 5
A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 5, pp. 695-711.
corrigé par Corrigendum for the comparison theorems in : “A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations” 
@article{AIHPC_2006__23_5_695_0,
     author = {Arisawa, Mariko},
     title = {A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {695--711},
     publisher = {Elsevier},
     volume = {23},
     number = {5},
     year = {2006},
     doi = {10.1016/j.anihpc.2005.09.002},
     mrnumber = {2259613},
     zbl = {1105.45004},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.002/}
}
TY  - JOUR
AU  - Arisawa, Mariko
TI  - A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2006
SP  - 695
EP  - 711
VL  - 23
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.002/
DO  - 10.1016/j.anihpc.2005.09.002
LA  - en
ID  - AIHPC_2006__23_5_695_0
ER  - 
%0 Journal Article
%A Arisawa, Mariko
%T A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2006
%P 695-711
%V 23
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.002/
%R 10.1016/j.anihpc.2005.09.002
%G en
%F AIHPC_2006__23_5_695_0
Arisawa, Mariko. A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 5, pp. 695-711. doi : 10.1016/j.anihpc.2005.09.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.002/

[1] Y. Achdou, O. Pironneau, Computational methods for option pricing, in preparation. | Zbl

[2] Alvarez O., Tourin A., Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (3) (1996) 293-317. | Numdam | MR | Zbl

[3] Arisawa M., Some ergodic problems for Hamilton-Jacobi equations in Hilbert space, Differential Integral Equations 9 (1) (1996) 59-70. | MR | Zbl

[4] M. Arisawa, Ergodic problems for a class of integro-differential equations, in preparation.

[5] Barles G., Buckdahn R., Pardoux E., Backward stochastic differential equations and integral-partial differential equations, Stochastics Stochastics Rep. 60 (1-2) (1997) 57-83. | MR | Zbl

[6] Bensoussan A., Lions J.L., Impulse Control and Quasi-Variational Inequalities, Gauthier-Villars, Paris, 1984. | MR

[7] Cont R., Tankov P., Financial Modelling with Jump Processes, Chapman and Hall/CRC, 2004. | MR | Zbl

[8] Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1) (1992). | MR | Zbl

[9] Framstad N.C., Oksendal B., Sulem A., Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs, J. Math. Econom. 35 (2) (2001) 233-257. | MR | Zbl

[10] Garroni M.G., Menaldi J.L., Second-Order Elliptic Integro-Differential Problems, Res. Notes Math., vol. 430, Chapmam and Hall/CRC, 2002. | MR | Zbl

[11] Gimbert F., Lions P.-L., Existence and regularity results for solutions of second-order elliptic integro-differential operators, Ricerche Mat. 33 (2) (1984) 315-358. | MR | Zbl

[12] C. Imbert, A non-local regularization of first order Hamilton-Jacobi equations, J. Differential Equations, in press. | MR | Zbl

[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). | MR | Zbl

[16] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, UK, 1999. | MR | Zbl

[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.

Cité par Sources :