Optimal prevention of large risks with two types of claims

Romain Gauchon (), Stéphane Loisel, Jean-Louis Rullière () and Julien Trufin
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Romain Gauchon: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Jean-Louis Rullière: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Julien Trufin: Département de mathématiques Université Libre de Bruxelles - ULB - Université libre de Bruxelles

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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 (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-02314914v2
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Published in Scandinavian Actuarial Journal, In press, 2021 (4), pp.323-334. ⟨10.1080/03461238.2020.1844791⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02314914

DOI: 10.1080/03461238.2020.1844791

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