Abstract: Optimizing reinsurance contracts is a big topic of study in the field of actuarial science from both theoretical and practical perspectives. Actuarial literature contains countless formulations and analytical results of what optimal reinsurance should mean for a single risk, but there is limited research on the optimal solution when the cedent runs many lines of business and asks to manage the risk effectively. In this paper, we extend the problem of optimal reinsurance to a multivariate framework where the cedent has multiple risks which cannot be bundled together into one. More specifically, we have chosen to solve the problem by using layer contracts and a more industrial based criterion, which is to balance risk and profit through a ratio where a risk measure is divided on expected surplus. Analytical results regarding the solution for the optimal parameters of multivariate risks are given in the paper. They suggest that in the bivariate case, with the expected premium principle, the solution is either balanced, with equal upper limits of the layers, or completely unbalanced, with one finite upper limit and one infinite one, corresponding to a stop-loss contract, depending on the marginal loss distributions. An extensive simulation study is also performed to confirm the analytical results, and extend them, in particular for a more general and realistic premium principle.

报告人简介：王吟之，西南财经大学金融学院副教授。2020年在挪威奥斯陆大学数学学院取得统计学博士学位（精算方向）。主要研究方向为最优再保险，非寿险准备金评估及统计模型在风险管理中的应用。主要研究成果发表在IME、NAAJ、SAJ等期刊上。