Risk Aversion

This chapter addresses the question under which conditions an RDU maximizer can be said to display risk aversion. Two concepts of risk aversion will be considered here. The first concept defines an individual to be risk averse if the sure gain E(F) of the expectation of a distribution F is always preferred to the distribution itself. An alternative definition of risk aversion, suggested by Rothschild and Stiglitz [1970], requires a risk averse individual to prefer a distribution F to any mean preserving spread of F. Obviously, a risk averter in the second sense is also risk averse in the sense of the first definition. It is well-known that in expected utility theory both concepts of risk aversion are equivalent to the concavity of the v.Neumann-Morgenstern utility function. However, the equivalence of the two notions of risk aversion does not carry over to general non-expected utility theories.