Self-protection with random costs

We study the consequences of introducing random costs (as opposed to certain costs) on the propensity to implement self-protection actions, i.e. actions reducing the probability of a loss. Our analysis is performed in four standard self-protection frameworks: (1) the one-period model in which the cost and benefit occur at the same period of time; (2) a variation of this one-period model where wealth in each state of nature is a random variable; (3) the one-period model where the cost of the self-protection action is only paid in the absence of loss; (4) the two-period model in which the cost of self-protection precedes its benefit. For each of these models we provide a set of conditions ensuring clear-cut effects to occur and a specific interpretation for each of them.