Abstract
<p style='text-indent:20px;'>We investigate the optimal reinsurance problems in this paper, specifically, the stop-loss strategies that can bring mutual benefit to both the insurance company and the reinsurance company. The utility improvement constraints are adopted by both contracting parties to guarantee that a reinsurance contract will bring higher expected utilities of wealth to the two participants. We also introduce five risk criteria that reflect the interests of both parties. Under each optimality criterion, we obtain explicit expressions of optimal stop-loss retentions and the corresponding optimised value of objective functions. The upper and lower bounds of expected utility increments under the optimal stop-loss retentions are provided. In the numerical example, we analyse the expected utility improvements under the criterion of minimising total Value-at-Risk. Notable increases in the lower bound of total utility increments are observed after adopting the joint utility improvement constraints.
Highlights
Reinsurance is the insurance among two insurance companies of contractual liabilities incurred under contracts of reinsurance
When investigating the expected utility increments under optimal stop-loss reinsurance that minimises the total VaR, we find that the insurance/reinsurance firm can suffer from utility decrements if we do not set up any constraints
When analysing the total utility increments of insurance firm and reinsurance firm, we find that in the worst case scenario, the optimal reinsurance strategies following utility constraints will always lead to more utility improvements than those without constraints
Summary
Reinsurance is the insurance among two insurance companies of contractual liabilities incurred under contracts of reinsurance. The idea of comparing expected utilities before and after reinsurance action is similar with [16], but their work focused on identifying the margins for achieving Pareto-optimal solutions in trading insurance risks While we use such idea to set up constraints and further study reinsurance optimisation under various criteria. There are quite a few literature investigating optimal reinsurance problems under risk measures such as VaR, CTE and TVaR, the readers may refer to [12], [14], and references therein Those studies are mainly from the point of view of the direct insurance company. Our work is different from [34], where the optimal reciprocal quota-share reinsurance strategies with mutual benefit is investigated, because we study the stop-loss reinsurance contract.
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