The constant elasticity of variance（CEV） model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theo...The constant elasticity of variance（CEV） model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant＇s whole life in the pension plan. Finally, two explicit solutions to exponential utility function in the two different periods （before and after retirement） are revealed. Hence, the optimal investment strategies in the two periods are obtained.展开更多
It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence...It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schr?dinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.展开更多
基金Project supported by the Science Foundation of Central South University of Forestry and Technology (No.06010A).
文摘The constant elasticity of variance（CEV） model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant＇s whole life in the pension plan. Finally, two explicit solutions to exponential utility function in the two different periods （before and after retirement） are revealed. Hence, the optimal investment strategies in the two periods are obtained.
基金supported by the Higher School Science and Technology Development Foundation of Tianjin(20100821)the Humanities and Social Science Research Youth Foundation of Ministry of Education (11YJC790006)
文摘It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schr?dinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.
