Optimal prevention of large risks with two types of claims

Abstract

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 intensity of large claims without impacting the small claims. We identify a necessary and sufficient condition for insurers to use prevention if there is no surplus. If, in addition, the severity of large claims dominates that of small claims by the harmonic mean residual life (HMRL) order, insurers invest more in prevention in the presence of a 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.

Keywords:

• Ruin theory
• prevention
• optimal prevention strategy
• insurance

Acknowledgments

This paper was realized within the framework of the Chair Prevent'Horizon, supported by the risk foundation Louis Bachelier and in partnership with Claude Bernard Lyon 1 University, Actuaris, AG2R La Mondiale, G2S, Covea, Groupama Gan Vie, Groupe Pasteur Mutualité, Harmonie Mutuelle, Humanis Prévoyance and La Mutuelle Générale. Romain Gauchon is employed by addactis France.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 For the following, prevention refers to self-protection, in the sense of Ehrlich & Becker (1972).

Additional information

Funding

This work was supported by Prevent Horizon and addactis France.