M. G. Crandall and H. Ishii, the maximum principle for semicontinuous functions, Diff. Int. Eqn, vol.3, pp.1001-1014, 1990.

M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society, vol.277, issue.1, pp.1-42, 1983.
DOI : 10.1090/S0002-9947-1983-0690039-8

C. Dellacherie and P. A. Meyer, Probabilités et potentiel. volume II : théorie des martingales, 1980.

N. Karoui, Les Aspects Probabilistes Du Controle Stochastique, Lect. Notes in Math, vol.876, pp.73-238, 1981.
DOI : 10.1007/BFb0097499

N. Karoui, J. Lepeltier, and A. Millet, A probabilistic approach to the reduite in optimal stopping, prbability and mathematical statistics, pp.97-121, 1992.

F. Gimbert and P. L. Lions, Existence and regularity results for solutions of second order integrodifferential operators, Ricerche Mat. XXXIII, issue.2, pp.315-358, 1984.

I. Karatzas and S. E. Shreve, Methods of mathematical finance, 1998.

M. Kobylanski, M. C. Quenez, and E. Rouy-mironescu, Optimal multiple stopping time problem, The Annals of Applied Probability, vol.21, issue.4, 2009.
DOI : 10.1214/10-AAP727

URL : https://hal.archives-ouvertes.fr/hal-00633327

P. Lions, Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application, Communications in Partial Differential Equations, vol.9, issue.10, pp.1101-1174, 1983.
DOI : 10.1080/03605308308820297

M. A. Maingueneau, Temps d???arret optimaux et theorie generale, pp.457-467, 1978.
DOI : 10.1007/BFb0064619

G. Peskir and A. Shiryaev, Optimal Stopping and Free-Boundary Problems, 2006.

H. Pham, Optimal stopping, free boundary, and American option in a jump-diffusion model, Applied Mathematics & Optimization, vol.60, issue.2, pp.145-164, 1994.
DOI : 10.1007/BF02683325

H. Pham, Optimal Stopping of Controlled Jump Diffusion Processes: A viscosity Solution Approach, Journal of Mathematical Systems, Estimation, and Control, vol.8, issue.1, pp.1-27, 1998.

A. Sayah, Equations d'Hamilton-Jacobi du premier ordre avec terme intégro-differentiels: Parties I et II, Comm. P.D.E, vol.10, pp.1057-1093, 1991.

H. M. Soner, Optimal Control with State-Space Constraint. II, SIAM Journal on Control and Optimization, vol.24, issue.6, pp.110-1122, 1986.
DOI : 10.1137/0324067