An old-new concept of convex risk measures: The optimized certainty equivalent
An old-new concept of convex risk measures: The optimized certainty equivalent
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DOI：
10.1111/j.1467-9965.2007.00311.x
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发表时间：
2007-07-01
影响因子：
1.6
通讯作者：
Teboulle, Marc
中科院分区：
文献类型：
--
作者：
Ben-Tal, Aharon;Teboulle, Marc
最优确定性等效（OCE）是作者于1986年首次提出的基于效用函数的决策理论准则。本文重新审视了这一基本概念，研究并扩展了其主要性质，并将其与最近的风险度量概念进行了比较。我们表明，负的OCE自然提供了一个广泛的家族的风险措施，适合凸风险措施的公理形式。对偶理论用于揭示OCE与phi-divergence泛函（相对熵的一种概括）之间的联系，并允许推导各种风险度量的变分公式。在对OCE的这种解释中，我们证明了最近在文献中分析和提出的几种风险度量（例如，风险的条件值，有界短缺风险）可以通过使用特定的效用函数推导出OCE的特殊情况。我们进一步研究了OCE和其他确定性等价物之间的关系，提供了这些可以被视为连贯/凸风险度量的一般条件。在整个论文中，几个例子说明了OCE在建筑风险度量方面的灵活性和充分性。
The optimized certainty equivalent (OCE) is a decision theoretic criterion based on a utility function, that was first introduced by the authors in 1986. This paper re-examines this fundamental concept, studies and extends its main properties, and puts it in perspective to recent concepts of risk measures. We show that the negative of the OCE naturally provides a wide family of risk measures that fits the axiomatic formalism of convex risk measures. Duality theory is used to reveal the link between the OCE and the phi-divergence functional (a generalization of relative entropy), and allows for deriving various variational formulas for risk measures. Within this interpretation of the OCE, we prove that several risk measures recently analyzed and proposed in the literature (e.g., conditional value of risk, bounded shortfall risk) can be derived as special cases of the OCE by using particular utility functions. We further study the relations between the OCE and other certainty equivalents, providing general conditions under which these can be viewed as coherent/convex risk measures. Throughout the paper several examples illustrate the flexibility and adequacy of the OCE for building risk measures.