Certainty Equivalent is a utility-based measure that performs as a measure in which investors are indifferent between this measure and investment that holds some uncertainty. Therefore, it plays an essential role in utility-based decision making. One of the most extensively used risk measures is the Value at Risk, which is investigated and used by both researchers and practitioners as a powerful tool that measures the risk under some quantile level which allows focusing on the extreme amount of losses. In this paper, we propose a natural generalization of the Certainty Equivalent measure that, similar to the Value at Risk measure, is focusing on the tail distribution of the risk, and thus, focusing on extreme financial and insurance risk events . We then investigate the fundamental properties of the proposed measure and show its unique features and implications in the risk measurement process. Furthermore, we derive formulas for truncated elliptical models of losses and provide formulas for selected members of such models.
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the Entropic Risk Measure in a unified way . We then investigate the fundamental properties of the proposed measure and show its unique features and implications in the risk measurement process. Furthermore, we derive formulas for truncated elliptical models of losses and provide formulas for selected members of such models.
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Certainty Equivalent is a utility-based measure that performs as a measure in which investors are indifferent between this measure and investment that holds some uncertainty. Therefore, it plays an essential role in utility-based decision making. One of the most extensively used risk measures is the
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the
R
which is investigated and used by both researchers and practitioners as a powerful tool that measures the risk under some quantile level which allows focusing on the extreme amount of losses. In this paper, we propose a natural generalization of the Certainty Equivalent measure that, similar to the
the Tail
R
measure, is focusing on the tail distribution of the risk, and thus, focusing on extreme financial and insurance risk events
and the Entropic Risk Measure in a unified way