Multivariate risk premiums

This paper develops characterizations of a risk premium and of the relation more risk averse, for multi-dimensional problems where the agent is exposed to an insurable and an uninsurable risk. We generalize and inter-relate results of Duncan (1977), Karni (1979), Kihlstrom et al. (1981), Malinvaud (1971), and Ross (1981) in deriving a local ordering of the risk aversion of agents with differing ordinal preferences.Earlier versions of this paper have been presented at seminars at New York University, the University of Alberta, and the University of British Columbia. We would like to acknowledge the helpful comments of participants at these presentations, in particular, Yakov Amihud, David Nachman, Joel Owen, Siegfried Schaible, Gordon Sick, and William Ziemba. All responsibility for errors and omissions resides with the authors.