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

 Access to full text

 Full (PDF)

1. [1] Y. Achdou, O. Pironneau, Computational methods for option pricing, in preparation. Zbl1078.91008
2. [2] Alvarez O., Tourin A., Viscosity solutions of nonlinear integro-differential equations, Ann. Inst. H. Poincaré Anal. Non Linéaire13 (3) (1996) 293-317. Zbl0870.45002MR1395674
3. [3] Arisawa M., Some ergodic problems for Hamilton–Jacobi equations in Hilbert space, Differential Integral Equations9 (1) (1996) 59-70. Zbl0848.35026MR1364034
4. [4] M. Arisawa, Ergodic problems for a class of integro-differential equations, in preparation. 
5. [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. Zbl0878.60036MR1436432
6. [6] Bensoussan A., Lions J.L., Impulse Control and Quasi-Variational Inequalities, Gauthier-Villars, Paris, 1984. MR756234
7. [7] Cont R., Tankov P., Financial Modelling with Jump Processes, Chapman and Hall/CRC, 2004. Zbl1052.91043MR2042661
8. [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). Zbl0755.35015MR1118699
9. [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. Zbl1013.91055MR1822346
10. [10] Garroni M.G., Menaldi J.L., Second-Order Elliptic Integro-Differential Problems, Res. Notes Math., vol. 430, Chapmam and Hall/CRC, 2002. Zbl1014.45002MR1911531
11. [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. Zbl0579.45010MR810193
12. [12] C. Imbert, A non-local regularization of first order Hamilton–Jacobi equations, J. Differential Equations, in press. Zbl1073.35059MR2121115
13. [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. [14] Miyahara Y., Minimal entropy martingale measure of jump type price processes in incomplete assets markets, Asia-Pacific Financial Markets6 (1999) 97-113. Zbl1153.91549
15. [15] Pham H., Optimal stopping of controlled jump diffusion processes; A viscosity solution approach, J. Math. Systems Estim. Control8 (1) (1998). Zbl0899.60039MR1650147
16. [16] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, UK, 1999. Zbl0973.60001MR1739520
17. [17] Sayah A., Equations d'Hamilton–Jacobi du premiere ordre avec termes integro-differentielles: parties 1 et 2, Comm. Partial Differential Equations16 (1991) 1053-1093. 

1. Mariko Arisawa, Corrigendum for the comparison theorems in : “A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations”
2. Guy Barles, Cyril Imbert, Second-order elliptic integro-differential equations : viscosity solutions' theory revisited