Optimal self-protection in two periods: On the role of endogenous saving

Abstract

Self-protection is a costly investment to reduce the probability of loss. This paper studies optimal self-protection in a two-period model with endogenous saving. In a setting with a binary loss we show that prudence is negatively associated with the optimal level of self-protection, consistent with results obtained in single-period models. We provide intuition for this finding with the help of a recent approach based on stochastic dominance. Furthermore, we determine the effect of interest rate risk on optimal self-protection and study a model in which a decision-maker engages in advance effort to increase the probability of facing a better risky situation. All our results suggest that the understanding of advance self-protection crucially hinges on whether the decision-maker also uses saving to optimize intertemporal consumption utility. If so, the fact that self-protection expenditures are upfront turns out to be irrelevant.