By applying the variational inequality technique, we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random ...By applying the variational inequality technique, we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity, boundedness and C^∞-smoothness of the exercise boundary are proved in this paper.展开更多
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 variation...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.展开更多
A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a par...A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.展开更多
基金the National Natural Science Foundation of China(Nos.10371045 and 10671075)the Natural Science Foundation of Guangdong Province(No.5005930)the Special Doctoral Program Foundation for Institution of Higher Education(No.20060574002)
文摘By applying the variational inequality technique, we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity, boundedness and C^∞-smoothness of the exercise boundary are proved in this paper.
基金the National Natural Science Foundation of China (Grant No.10671075)the National Natural Science Foundation of Guangdong Province (Grant No.5005930)the University Special Research Fund for PhD Program (Grant No.20060574002)
文摘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.
基金supported by National Natural Science Foundation of China(10901060,10971073,1081056)Natural Science Foundation of Guangdong Province (9451063101002091)
文摘A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.
