A Parabolic Obstacle Problem Related To Executive Stock Options

In this paper, we have studied that the following form of a parabolic obstacle problem exist solution.where r,σ,μ,K,γ,l和L are all positive numbers ,and c and d are constant,with c＜lnK＜d,ξ(z)is the given function ,to meetξ∈C~∞([c, d]) ,ξ(z)＜0 in [c, d],andwhere 0＜v＜d－ln K.This problem comes from executive stock options on the best implementation strategy, and its characteristics are: there exists (?) at obstacle condition Bu≥0, which makes more difficult to research this problem.In this paper, we have used slicing method to study.We discrete the time variable (?) to approach the above-mentioned parabolic obstacle problem. We have proved the existence of the solution in (?) through estimating the approximate solution,whereQ=(c,d)×(l,L).