Optimal prevention of large risks with two types of claims.

Summary In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the large claims intensity without impacting the small claims. In this setting, we prove that prevention is advantageous when claim severities for small and large claims are ordered in the sense of the Harmonic-Mean-Residual-Lifetime (HMRL) order. In addition, we show that the optimal prevention amount is the lowest when there is no initial surplus. Finally, we characterize the asymptotic optimal prevention strategy when the initial surplus tends to infinity in the two main cases where both claim types are light-tailed and where one of them is light-tailed and the other one is heavy-tailed.