一个描述金融投资项目演化的量子力学状态方程

Quantum mechanical state equation for describing evolution of projects of financial investment

本文提出了一个描述金融投资项目演化的量子力学状态方程,该方程的参数比较好地模拟了金融市场的基本要素,包括投资(输入)、资产损耗(缩水)、资产增益、和收益(输出)等,方程中的量子力学算符也能够反映该项目的动力学过程与特征,所以能代表一类金融投资项目(其状态用Dirac符号表示)在市场中的演化模式.通过引入纠缠态表象得出了该方程的量子解(算符之和形式),该量子解给出了初态与终态的联系,也就给出了投资项目的动态过程.作为例子,求出单一投资项目在金融市场中的演化,不但得出了符合市场演化趋势的解,而且提出了二项-负二项纠缠态.在推导过程中,充分利用了Dirac符号和有序算符内的积分技术(IWOP).

This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment （input）, assets loss （assets decrease）, assets increase and income （output）, the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac’s symbolic method and the technique of integration within an ordered product （IWOP） of operators.