圣彼得堡悖论新解——比例效用理论溯源经典

New Explanation on St. Petersburg Paradox——Based on Ratio Utility Theory

回顾效用理论300年发展历程,一个被忽视百余年的经典决策机制再次呈现。为此,探索了该经典决策机制基础上的新决策理论体系,构建了一个新的风险资产定价模型,并且对圣彼得堡悖论作出了新的量化解释。初步得出以下结论:(1)个人的决策依据是财富增量与财富最终持有量的比值,即比例效用;(2)比例效用具有两个重要推论,即边际效用递减和损失厌恶;(3)比例效用没有下限;(4)投资者的初始财富数量越大,投资于风险资产的倾向越高;(5)投资者的经验越丰富,投资于风险资产的倾向越高;(6)独立评估圣彼得堡风险资产条件下,投资者的报价上限为1.5;(7)比例效用视角下,不会存在衍生的圣彼得堡悖论。

A new quantitative explanation on St. Petersburg paradox can be derived from a classic decision idea which has been ignored for centuries. Several conclusions can be presented： （1）the ratio of the incremental wealth to the final wealth is the determinant for people to make decision, which can be named Ratio utility; （2） marginal utility diminishing and loss aversion can be inferred from Ratio utility principle; （3）there is no lower limit for the Ratio utility; （4）the more wealth the investors have, the higher risk the investors tend to take; （5） the more experienced the inventors are in participating in risk investment, the more frequent the inventors tend to do risk investments; （6）the prices provided for Petersburg game will be maximum 1.5 based on authentic ratio utility; （7） from the aspect of Ratio Utility, the Super St. Petersburg paradox will not exist.