Self-protection with random costs

Abstract

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.

Optimal Investment of Defined Contribution Pension Based on Self-Protection and Minimum Security

“…In Ref. [12], when faced with a possible risk, sometimes people make efforts to reduce the loss. This behavior is called defense or self-protection.…”

“…Liu et al [11] studied a different cycle model, which considers that decision makers, when faced with risk, only pay the cost of effort in self-protection if no loss occurs ("conditional payout"). Finally, Crainich and Menegatti [12] studied the propensity and impact of introducing random costs (as opposed to deterministic costs) on the implementation of self-protection actions. The analysis by Crainich and Menegatti [12] is carried out under the framework of four standard self-preservation, but they do not give an analytical solution.…”

“…Finally, Crainich and Menegatti [12] studied the propensity and impact of introducing random costs (as opposed to deterministic costs) on the implementation of self-protection actions. The analysis by Crainich and Menegatti [12] is carried out under the framework of four standard self-preservation, but they do not give an analytical solution.…”

“…This paper will introduce a self-protection framework in Ref. [12] on the basis of Ref. [8], and assume that the cost of self-protection is certain, and investors only pay the cost of self-protection when no loss occurs.…”