Abstract
In this paper we present a method which can transform a variational inequality with gradient constraints into a usual two obstacles problem in one dimensional case. The prototype of the problem is a parabolic variational inequality with the constraints of two first order differential inequalities arising from a two-dimensional model of European call option pricing with transaction costs. We obtain the monotonicity and smoothness of two free boundaries.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10671075), the National Natural Science Foundation of Guangdong Province (Grant No. 5005930), and the University Special Research Fund for PhD Program (Grant No. 20060574002)
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Yi, F., Yang, Z. A variational inequality arising from European option pricing with transaction costs. Sci. China Ser. A-Math. 51, 935–954 (2008). https://doi.org/10.1007/s11425-007-0175-4
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DOI: https://doi.org/10.1007/s11425-007-0175-4