We present a necessary and sufficient condition on an agent's utility function for a simple mean preserving spread in an independent background risk to increase the agent's risk aversion (incremental risk vulnerability). Gollier and Pratt (1996) have shown that declining and convex risk aversion...

In this paper, we derive an equilibrium in which some investors buy call/put options on the market portfolio while others sell them. Also, some investors supply and others demand forward contracts. Since investors are assumed to have similar risk-averse preferences, demand for these contracts is...