A localization of the L{é}vy operators arising in mathematical finances
arXiv:1012.3108
Abstract
The comparison principle and the existence of the solution of the integro-differential equation with L{é}vy operators, in the framework of the viscosity solution, are shown in this paper. For the one dimensional case, a detailed estimate of the H{ö}lder continuity of solutions is presented, by localizing the singularity of the L{é}vy measure.