An old-new concept of convex risk measures: The optimized certainty equivalent

被引:228
作者
Ben-Tal, Aharon
Teboulle, Marc [1 ]
机构
[1] Tel Aviv Univ, Sch Math Sci, IL-69978 Ramat Aviv, Israel
[2] Technion Israel Inst Technol, IL-32000 Haifa, Israel
关键词
expected utility; certainty equivalents; coherent risk measures; convex risk measures; risk aversion; convex duality; information theory; phi-divergences; decision making under uncertainty; conditional value at risk; penalty functions; shortfall risk;
D O I
10.1111/j.1467-9965.2007.00311.x
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
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.
引用
收藏
页码:449 / 476
页数:28
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