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MR2667314 91G20 (60B10 60F17 60H07)
Kulik, O. M.; Mīshura, Yu. S.; Soloveĭko, O. M. Convergence with respect to the parameter of a series and the differentiability of barrier option prices with respect to the barrier. (Ukrainian) Teor. Ĭmovīr. Mat. Stat. No. 81 (2009), 102--113; translation in Theory Probab. Math. Statist. No. 81 (2009), 117–130
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