Standard Risk Aversion and the Demand for Risky Assets in the Presence of Background Risk

We consider the demand for state contingent claims in the presence of a zero-mean, nonhedgeable background risk. An agent is defined to be generalized risk averse if he/she reacts to an increase in background risk by choosing a demand function for contingent claims with a smaller slope. We show that the conditions for standard risk aversion: positive, declining absolute risk aversion and prudence are necessary and sufficient for generalized risk aversion. We also derive anecessary and suÆcient condition for the agent's derived risk aversion to increase with a simple increase in background risk.