Increased Risk Bearing with Background Risk
Topics in Theoretical Economics, Vol. 6, No. 1, Article 3
Posted: 13 Sep 2006
Many analyses of risk taking behavior assume that an agent faces only a single risk. Typically, however, an agent faces many risks simultaneously, and the interaction between risks may well affect how much of any particular risk an agent should bear. Ross (1981) and Kihlstrom, Romer, and Williams (1981) showed that the comparative statics of increased risk aversion in the two asset portfolio model are not robust to the addition of background risk, even under strong independence assumptions between the risks. In this paper we give sufficient and necessary conditions on changes in a risky asset's distribution that increase risk taking in the presence of background risk. We find that the comparative statics of changes in risk are fairly robust to background risk. We present results for changes in each of the conditional distributions of the primary risk (keeping the marginal distribution of the background risk fixed) and for changes in the marginal distribution of the primary risk (keeping each conditional distribution of the background risk fixed). For the former question a modification of Gollier's (1995) Linear Stochastic Dominance is necessary and sufficient; for the latter Monotone Likelihood Ratio Dominance is necessary and sufficient. We also consider other applications, including the two risky asset portfolio problem.
Keywords: comparative statics under uncertainty, risk taking, background risk, monotone likelihood ratio order, greater central riskiness, multivariate risk
JEL Classification: D8
Suggested Citation: Suggested Citation