A Note on Partial Insurance and the Arrow-Pratt Measure of Risk Aversion

Pratt [1964] establishes that a more risk-averse individual in the Arrow-Pratt sense has a higher compensating risk premium for full insurance, but no comparable result has been established for partial insurance. Ross [1981] shows that a more risk-averse individual in the Arrow-Pratt sense may not be willing to pay more for a reduction in risk in the sense of mean-preserving contraction. We show that a more risk-averse individual in the Arrow-Pratt sense has a higher compensating risk premium for all empirically relevant forms of partial insurance because they induce a reduction in risk in the stronger sense of Bickel and Lemann [1979]. Copyright The Geneva Association 2005