Before revision: 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.
After revision: 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, 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.