Multiplicative background risk

Although there has been much attention in recent years on the effects of additive background risks, the same is not true for its multiplicative counterpart. We consider random wealth of the multiplicative form &xmacr;&ymacr;, where &xmacr; and &ymacr; are statistically independent random variables. We assume that &xmacr; is endogenous to the economic agent but that &ymacr; is an exogenous and nontradable background risk that represents a type of market incompleteness. Our main focus is on how the presence of the multiplicative background risk &ymacr; affects risk-taking behavior for decisions on the choice of &xmacr;. We extend the results of Gollier and Pratt to characterize conditions on preferences that lead to more cautious behavior.