Locally Greater Vulnerability to Background Risk

Willingness to take on risk is influenced by the presence of fair and unfair background risks for decision makers who are risk vulnerable as defined by Gollier and Pratt 1996], for these decision makers are more risk averse when they possess such an uninsurable background risk. We present an alternative derivation of the index of local vulnerability based on Diamond and Stiglitz 1974] compensated increases in risk, such that risk aversion increases with the introduction of any small fair background risk if and only if the index of local vulnerability is positive. We establish that the increase in risk aversion is greater for those who are more vulnerable as measured by the index of local vulnerability.