Optimal reinsurance with positively dependent risks

Jun Cai and Wei Wei

Insurance: Mathematics and Economics, 2012, vol. 50, issue 1, 57-63

Abstract: In the individual risk model, one is often concerned about positively dependent risks. Several notions of positive dependence have been proposed to describe such dependent risks. In this paper, we assume that the risks in the individual risk model are positively dependent through the stochastic ordering (PDS). The PDS risks include independent, comonotonic, conditionally stochastically increasing (CI) risks, and other interesting dependent risks. By proving the convolution preservation of the convex order for PDS random vectors, we show that in individualized reinsurance treaties, to minimize certain risk measures of the retained loss of an insurer, the excess-of-loss treaty is the optimal reinsurance form for an insurer with PDS dependent risks among a general class of individualized reinsurance contracts. This extends the study in Denuit and Vermandele (1998) on individualized reinsurance treaties to dependent risks. We also derive the explicit expressions for the retentions in the optimal excess-of-loss treaty in a two-line insurance business model.

Keywords: IM30; IM52; IB92; Dependent risk; Positive dependence; PDS; Convex order; Individualized reinsurance treaty; Optimal reinsurance (search for similar items in EconPapers)
JEL-codes: C02 C60 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (24)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:50:y:2012:i:1:p:57-63

DOI: 10.1016/j.insmatheco.2011.10.006

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