Certainty equivalent measures of risk

We study a framework for constructing coherent and convex measures of risk that is inspired by infimal convolution operator, and which is shown to constitute a new general representation of these classes of risk functions. We then discuss how this scheme may be effectively applied to obtain a class of certainty equivalent measures of risk that can directly incorporate preferences of a rational decision maker as expressed by a utility function. This approach is consequently employed to introduce a new family of measures, the log-exponential convex measures of risk. Conducted numerical experiments show that this family can be a useful tool for modeling of risk-averse preferences in decision making problems with heavy-tailed distributions of uncertain parameters.