A localization of the L{é}vy operators arising in mathematical finances

Details A localization of the L{é}vy operators arising in mathematical finances A localization of the L{é}vy operators arising in mathematical finances

2010-12-14

arxiv.org/abs/1012.3108v1

Stochastic processes and Applications to Mathematical Finances, 6th RITS symposium, ed., S. Ogawa, J. Akahori, S. Watanabe, Wo

Mathematics

Analysis of PDEs

Scientific paper

The comparison principle and the existence of the solution of the
integro-differential equation with L{\'e}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{\"o}lder continuity of solutions is presented, by
localizing the singularity of the L{\'e}vy measure.

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