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In this paper we explore an identity in distribution of hitting times of afinite variation process (Yor's process) and a diffusion process (geometricBrownian motion with affine drift), which arise from various applications infinancial mathematics. As a result, we provide analytical solutions to the faircharge of variable annuity guaranteed minimum withdrawal benefit (GMWB) from apolicyholder's point of view, which was only previously obtained in theliterature by numerical methods. We also use complex inversion methods toderive analytical solutions to the fair charge of the GMWB from an insurer'spoint of view, which is used in the market practice, however, based on MonteCarlo simulations. Despite of their seemingly different formulations, we canprove under certain assumptions the two pricing approaches are equivalent.

An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit