@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://www.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://www.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://www.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://www.numdam.org/articles/10.1016/j.anihpc.2005.09.002/
[1] Y. Achdou, O. Pironneau, Computational methods for option pricing, in preparation. | Zbl
[2] Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (3) (1996) 293-317. | Numdam | MR | Zbl
, ,[3] 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] Backward stochastic differential equations and integral-partial differential equations, Stochastics Stochastics Rep. 60 (1-2) (1997) 57-83. | MR | Zbl
, , ,[6] Impulse Control and Quasi-Variational Inequalities, Gauthier-Villars, Paris, 1984. | MR
, ,[7] Financial Modelling with Jump Processes, Chapman and Hall/CRC, 2004. | MR | Zbl
, ,[8] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1) (1992). | MR | Zbl
, , ,[9] Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs, J. Math. Econom. 35 (2) (2001) 233-257. | MR | Zbl
, , ,[10] Second-Order Elliptic Integro-Differential Problems, Res. Notes Math., vol. 430, Chapmam and Hall/CRC, 2002. | MR | Zbl
, ,[11] 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] Minimal entropy martingale measure of jump type price processes in incomplete assets markets, Asia-Pacific Financial Markets 6 (1999) 97-113.
,[15] Optimal stopping of controlled jump diffusion processes; A viscosity solution approach, J. Math. Systems Estim. Control 8 (1) (1998). | MR | Zbl
,[16] Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, UK, 1999. | MR | Zbl
,[17] 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 :