Are quantile risk measures suitable for risk-transfer decisions?

Although controversial from the theoretical point of view, quantile risk measures are widely used by institutions and regulators.In this paper, we use a unified approach to find the optimal treaties for an agent who seeks to minimize one of these measures, assuming premium calculation principles of various types.We show that the use of measures like Value at Risk or Conditional Tail Expectation as optimization criteria for insurance or reinsurance leads to treaties that are not enforceable and/or are clearly bad for the cedent. We argue that this is one further argument against the use of quantile risk measures, at least for the purpose of risk-transfer decisions.

► Optimal treaties for quantile risk measures are considered. ► Optimal treaties are often not enforceable and/or are obviously bad for the cedent. ► Under certain premiums the cedent makes a loss almost certainly. ► We argue that quantile risk measures are not appropriate for risk-transfer decisions.