# Project 4: Risk Aversion in Additive Multivariate Utility Functions

Contact: Nikolaos Argyris, Johannes Jaspersen, Andreas Richter

**Abstract:**

Additive multivariate utility functions are common in applications of economic decision-making. They exist in many areas of multi-criteria decisions and are prominently featured in intertemporal decision problems. However, the concept of risk aversion in such functions is poorly understood. In this paper, we formally show the previously posited result that it is impossible to compare two additive multivariate utility functions solely with respect to their risk aversion regarding one or more attributes. We then introduce the class of contextual additive multivariate utility functions in which some monotonicity properties of risk aversion regarding a single attribute are maintained and ordinal preferences change in a sensible manner. We show three applications of this class of functions: the effect of increased risk aversion on non-monetary prevention, risk premiums in a Köszegi-Rabin decision model and risk premiums in cumulative prospect theory.