On the existence of a representative reinsurer under heterogeneous beliefs

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.

Optimal Insurance Contracts Under Distortion Risk Measures With Ambiguity Aversion

“…Thus, the problem becomes a special case of a more general optimal insurance problem with heterogeneous beliefs, which was studied, for example, by Boonen (2016) and Boonen and Ghossoub (2019). In particular, Boonen and Ghossoub (2019) considered one insurer and multiple reinsurers who have different distributional assumptions. For comparison, we note that this paper assumes that there is only one insured and one insurer.…”

Mean–variance Insurance Design With Counterparty Risk and Incentive Compatibility

“…Under various objective functions and premium principles and taking into account of more sophisticated economic factors, considerable advancements have been achieved in the literature. We refer to Chi and Tan (2011), Chi (2012), Cheung et al (2019), Ghossoub (2019b), Boonen and Ghossoub (2019) for recent developments.…”

Pareto-optimal insurance contracts with premium budget and minimum charge constraints

“…They studied unilateral optimal insurance problems via optimizing the buyer's variance and expected utility respectively. A vast literature has been readdressing their proposed unilateral optimal insurance problems via various objective functions in [6,11,14,16,17,20,31,32,34], premium principles in [12,15], practical constraints in [13,23,27,28,35,36,37], and more recently, heterogeneous beliefs in [7,18,24], as well as background risks in [19]; see also a recent work [22], and the references therein.…”