Cross‐Prudence and Optimal Prevention

ABSTRACT In this paper, we study optimal prevention in the presence of a correlated nonfinancial background risk. Under positive correlation, cross‐prudence in the nonfinancial attribute reduces optimal prevention. We establish this result in the most direct extension of the standard prevention problem with binary marginal distributions and show that it extends to richer settings. Our analysis highlights a broader implication: in economically relevant cases with loss probabilities below one‐half and positive correlation, cross‐prudence emerges as an additional force that discourages prevention. As a result, optimal prevention can fall below the expected‐cost minimizing level, even when agents are risk‐averse.