期望效用与效用分位数组合决策准则研究

Research on decision criteria combining expected utility and utility quantiles

将期望效用决策模型和效用分位数决策模型进行组合,提出了期望效用分位数决策准则(简记为EU-Q决策准则)。其拓展了期望效用决策准则以及效用分位数决策准则,是秩相依期望效用函数的一类推广形式。验证了EU-Q决策准则遵循理想决策准则的基本公理,包括客观性、单调性、连续性和弱序性等;证明了在此决策准则下,决策者为风险厌恶型或者风险偏好型应满足的条件,以及效用函数经过平移或者缩放变换不会改变决策者对备选方案的排序。EU-Q决策准则结合了期望效用决策准则和效用分位数决策准则的特点和优势,不仅能较好地解释Allais等悖论,而且还能解释期望效用与香农熵、方差等不同度量准则的组合决策模型无法解释的问题。EU-Q决策准则具有丰富的理论内涵和较强的解释力,适用解决不确定性决策问题。

The paper combines the expected utility decision model and the utility quantile decision model,proposing the Expected Utility-Quantile(EU-Q)decision criterion,which is an extension of both the expected utility criterion and the utility quantile decision criterion,and represents a generalization of rank-dependent expected utility functions.It verifies that the EU-Q decision criterion adheres to the basic axioms of ideal decision criteria,including objectivity,monotonicity,continuity,and weak orderliness.It also proves the conditions that decision-makers should meet if they are risk-averse or risk-seeking,and that the utility function’s translation or scaling transformation does not change the decision-maker’s ranking of alternative options.The EU-Q decision criterion integrates the characteristics and advantages of both the expected utility criterion and the utility quantile decision criterion,not only providing a good explanation for paradoxes such as the Allais paradox,but also addressing problems that cannot be explained by decision models combining expected utility with measures like Shannon entropy and variance.The EU-Q decision criterion has rich theoretical characteristics and strong explanatory power,making it suitable for solving decision-making problems with uncertainty.