Vigilance, Risk Vulnerability, and the Precautionary Augment

Risk raises the expected marginal utility of a prudent agent. We define this proportional change as the precautionary augment, which measures risk-induced changes in the marginal value of saving, the Lucas Tree risk-free rate, and asset prices in a derivative-saturated market where market-state securities provide incomplete coverage against idiosyncratic risk. One agent is more vigilant than another if their precautionary augment is larger for all unfair risks. We derive and compare conditions for greater vigilance, showing how to implement the Diffidence Theorem geometrically. Because risk vulnerability is equivalent to decreasing vigilance, classic results about risk vulnerability emerge as corollaries.