Econ Papers Daily / 期刊论文
论货币的效用函数
On Utility Functions for Money
摘要
In choice under risk, the curvature of Bernoulli utility function for money captures attitudes towards risk (under expected utility theory). Two popular functional forms for Bernoulli utility are an exponential function, which exhibits constant absolute risk aversion, and a power function, which exhibits constant relative risk aversion. Both struggle to capture a relatively high risk aversion over large stakes coexisting with a relatively low risk aversion over small stakes. This note presents a new utility function for money expressed via the modified Bessel function of the second kind that overcomes this problem. This utility function exhibits a constant coefficient xu(x)’’/u(x).
中文摘要
在风险选择中，货币伯努利效用函数的曲率（在期望效用理论下）体现了风险态度。两种流行的伯努利效用函数形式是指数函数，其表现出恒定绝对风险厌恶，以及幂函数，其表现出恒定相对风险厌恶。二者都难以刻画在大额赌注上相对较高的风险厌恶与在小额赌注上相对较低的风险厌恶并存的情况。本文提出了一种通过第二类修正贝塞尔函数表示的新的货币效用函数，克服了这一问题。该效用函数表现出恒定系数 xu(x)’’/u(x)。