一种随机特殊函数方程的解法及定常风险厌恶效用函数的导出

A Method of Solving the Special Functional Equation Including a Random Variable and a Process of Deriving Constant Risk-Averse Utility Function

为建立风险分析模型构造出一种含随机变量X的特殊函数方程f(f^-1(E(f(X)))+y)＝E(f(X+Y))，目前尚未有统一解法．本文通过一系列变换给出了它的一般解：并导出一种用于风险决策分析的效用函数，且对该函数的参数性质进行了界定．

This paper structured the special functional equation including a random variable for modle building to rish analysis f(f^-1(E (f(X))) +y)=E (f(X+y)). The equation can not be solved by now available theories. The paper devclops a method of solving it, then derives the utility function for decision analysis from the process of solving the equation, and regularizes the properties of parameters of the utility function .