Increased risk-bearing with background risk

Analyses of risk-bearing often assume that agents face only one risk. Agents however usually face several risks and the interaction between them can affect the willingness to bear any one of them. We consider how the introduction of background risk affects the comparative statics predictions of distribution changes in the standard two asset portfolio model. We show that such predictions are fairly robust, no matter what the correlation between the two risks. We consider changes in the conditional distributions of the risky asset's return; and changes in the marginal distribution of the asset's return. For the first question, a version of Gollier's (1995) Central Riskiness order is sufficient and necessary to increase risk-bearing. For the second question, Monotone Likelihood Ratio improvements are sufficient and necessary. Many of our proofs illustrate the "basis" approach to comparative statics under uncertainty.