尼尔森的弱损失厌恶与强损失厌恶：一种刻画及广义累积前景理论效用函数
Neilson's Weak vs. Strong Loss Aversion: A Characterization and a Generalized CPT-Utility Function
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中文总结 AI 辅助
研究风险下多目标多标准决策中尼尔森的损失厌恶定义，通过理论分析明确强弱概念的条件，指出相关效用函数局限，提出广义CPT效用函数，扩展其描述范围并提供用于分析和优化的函数形式。
中文摘要 AI 辅助
在风险下的多目标和多标准决策中，尤其是涉及个体行为的情况下，基于主观评估的风险感知分析愈发重要。累积前景理论（CPT）超越风险中性建模和预期效用理论（EUT）的限制，提供了一个基于行为的框架。本文对尼尔森的厌恶定义进行了严格理论分析，给出基于赌博的解释，明确强弱概念重合及分歧条件。还研究了相关效用函数及标准CPT规范的结构局限与不一致性。为此提出广义CPT效用函数，扩展了CPT描述范围，为敏感性分析和基于效用函数的优化提供了有用的函数形式。
英文摘要
In multi-objective and multi-criteria decision-making under risk, especially in settings involving individual behavior, risk-aware analysis based on subjective evaluation has become increasingly important. Moving beyond risk-neutral modeling and the constraints of Expected Utility Theory (EUT), Cumulative Prospect Theory (CPT) provides a behaviorally grounded framework for capturing how individuals perceive and evaluate risky prospects. This paper conducts a rigorous theoretical analysis of Neilson's definitions of aversion. We provide a gamble-based interpretation, sharpen key conceptual distinctions, and make explicit the conditions under which the weak and strong notions coincide as well as when they diverge. Furthermore, we examine the Kobberling-Wakker utility function and related standard CPT specifications, highlighting structural limitations and inconsistencies that arise when these forms are required to satisfy Neilson-type aversion conditions. To address these issues, we propose a generalized CPT-utility function that retains the canonical reference-dependent shape while offering additional flexibility. This generalization extends the descriptive scope of CPT and provides an explicit functional form that is useful for sensitivity analysis and utility function-based optimization.
