Marti G Subrahmanyam, Günter Franke, Richard C Stapleton
ABSTRACT
We establish a necessary and sufficient condition for the risk aversion
of an agent's derived utility function to increase with independent, zero-mean
background risk. This condition is weaker than standard risk aversion.
For small risks, the condition is that the ratio of the third to the first
derivative of the utility function is decreasing in income. In a market
with state-contingent marketable claims, an increase in background risk,
which raises the agent's derived risk aversion, reduces the slope of the
agent's optimal sharing rule. Under a weak aggregation condition, an increase
of background risk for many agents in the economy raises the prices of
marketable claims in states with a low level of marketable aggregate income
relative to the prices in states with a higher level of such income.
Subrahmanyam: (212) 998-0348 msubrahma@stern.nyu.edu
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