Coherent measures of risk defined by the axioms of monotonicity, subadditivity, positive homogeneity, and translation invariance are recent tools in risk management to assess the amount of risk agents are exposed to. If they also satisfy law invariance and comonotonic additivity, then we get a subclass of them: spectral measures of risk. Expected shortfall is a well-known spectral measure of risk.we investigate the above mentioned six axioms using tools from general equilibrium (ge) theory. Coherent and spectral measures of risk are compared to the natural measure of risk derived from an exchange economy model, which we call the ge measure of risk. We prove that ge measures of risk are coherent measures of risk. We also show that spectral measures of risk are ge measures of risk only under stringent conditions, since spectral measures of risk do not take the regulated entity’s relation to the market portfolio into account. To give more insights, we characterize the set of ge measures of risk via the pricing kernel property.
Csóka, P., Herings, P. J. J., & Kóczy, L. Á. (2007). Coherent measures of risk from a general equilibrium perspective. Journal of Banking & Finance, 31, 2517-2534. https://doi.org/10.1016/j.jbankfin.2006.10.026