Should more risk-averse agents exert more effort?

Consider an agent facing a risky distribution of losses who can change this distribution by exerting some effort. Should he exert more effort when he becomes more risk-averse? For instance, should we expect more risk-averse drivers to drive more cautiously? In this article, we give sufficient conditions under which the answer is positive, using results presented in Jewitt (1989). We first extend the standard models of self-insurance and self-protection and show that the comparative statics depends only on the effect of effort on the net loss. We then present conditions for the continuous case with applications.