Extropy风险度量及应用

Extropy Risk Measure and Its Applications

摘要: 为了解决风险喜爱随机优化问题，给风险喜爱投资者的投资行为提供帮助，基于信息理论中的熵提出了Extropy风险度量(ExRMc)，并对其性质从理论和应用两个方面进行了研究。理论研究表明Extropy风险度量是一个具有一致性且风险偏好的度量，而且关于参数c具有连续性、可微性与鲁棒性。投资组合选取问题的应用研究表明：ExRMc考虑了风险收益平衡，且与随机比较中的3阶递增凸序相一致，是一个合理的风险度量。最后把ExRMc风险度量应用于解决风险喜爱随机优化问题，得到了一个全有或全无的决策。这些主要结果表明Extropy风险度量补充了传统期望效用理论中风险度量的不足，合理地解释了银行对于信贷与现金持有之间的典型商业决策时，要么不发放任何贷款要么全部选择信贷的行为。

Abstract: To solve the risk-loving stochastic optimization problems and provide assistance for risk-loving investors’ investment behavior, Extropy risk measure is proposed based on entropy in information theory and its important properties are studied respectively from theory and application. Theoretical research shows that it is a measure with consistency and risk-loving preference, and is continuous, differentiable, and robust on parameter c. The research on application of portfolio selection problem shows that it is a reasonable risk measure with balance between risk and return and is consistent with the 3rd order increasing convex order in random comparison. Finally, it is applied into solving out risk-loving stochastic optimization problem, which yields an all or nothing decision. These results illustrate that Extropy risk measure can be an efficient supplement of risk measure in the traditional expected utility theory and can formally explain the banks’ behavior of either not issuing any loans or choosing credit for all when they make typical commercial decisions between credit and cash holdings.