On the existence of a representative reinsurer under heterogeneous beliefs

Tim J. Boonen and Mario Ghossoub

Insurance: Mathematics and Economics, 2019, vol. 88, issue C, 209-225

Abstract: This paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer’s risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen et al. (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we derive optimal reinsurance contracts in case the insurer maximizes dual utility, or in case the insurer maximizes a generic objective that preserves second-order stochastic dominance under the assumption of a monotone hazard ratio.

Keywords: Optimal reinsurance design; Heterogeneous beliefs; Multiple reinsurers; Representative reinsurer; Deductible (search for similar items in EconPapers)
JEL-codes: D86 G22 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:88:y:2019:i:c:p:209-225

DOI: 10.1016/j.insmatheco.2019.07.008

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