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本文主要应用PDE方法对俄式期权定价问题进行理论分析.类似于美式期权定价问题,俄罗斯期权定价问题可归结为一个一维抛物型变分不等式.我们首先引入惩罚函数证明了该变分不等式的解的存在唯一性,然后研究了自由边界的一些性质,如单调性、光滑性和自由边界的位置.
In this paper, the PDE method is mainly applied to the theoretical analysis of the Russian option pricing problem.Compared with the American option pricing problem, the Russian option pricing problem can be attributed to a one-dimensional parabolic variational inequality.First, we introduce the penalty function to prove the variational inequality The existence and uniqueness of the solutions are then studied. Some properties of the free boundary, such as monotonicity, smoothness and the position of the free boundary, are then studied.