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Idiosyncratic risk, sharing rules, and the theory of risk bearing

Günter Franke (), Richard C. Stapleton and Marti G. Subrahmanyam

No 181, Discussion Papers, Series II from University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy"

Abstract: The choice of an agent between risky and riskless assets is complicated by the existence of idiosyncratic risk. In this paper the agent chooses state-dependent shares of aggregate marketable income (a sharing rule) to provide a partial hedge against the idiosyncratic risk. The agent's Utility function exhibits positive, decreasing absolute risk aversion and prudence. Then the higher the idiosyncratic risk, the more the agent purchases claims in states with low aggregate income and the less in states with high aggregate income. The sensitivity of the equilibrium to an increase in the idiosyncratic risk across all investors is analyzed. These results are made more specific by considering the special case of the Hyperbolic Absolute Risk Aversion (HARA) family of Utility functions. In this case, the precautionary premium can be defined more precisely and the sharing rules can be derived explicitly.

Date: 1992
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