Some developments on optimal reinsurance problem relating to ruin probability

报告摘要：In this work, we investigate the optimal per-claim reinsurance problem to minimize the insurer's ruin probability. Inspired by the exponential upper bound of ruin probability in Cramér-Lundberg model, we take Lundberg exponent maximization as the value function. In the first part, we consider the optimal reinsurance problem under the combined upper moment premium principle. In the second part, we consider the optimal reinsurance problem for an insurer who has different belief about claims with the reinsurer based on the perspective of risk control. With the technique of piecewise modification, we extend the method adopted in Tan et al. [European J. Oper. Res., 282(2020), pp. 345-362] and Meng et al. [SIAM J. Financial Math., 13(2022), pp. 903-943]. This approach proposed here has good applicability for modifying reinsurance candidate to satisfy the incentive compatibility condition based on other value functions, such as the utility maximization problem. As examples, we also present the explicit reinsurance structures under a few representative belief heterogeneity environments.

报告人简介： 孟辉，中央财经大学中国精算研究院/保险学院教授，博士生导 师，中央财经大学“青年龙马学者”。研究方向包括保险精算，金融风险分析与决 策等，主持多项国家自然科学基金面上项目和中央财经大学创新团队项目，在《SIAM Journal on Control Optimization》、《SIAM Journal on Financial Mathematics》、 《Economic Modelling》、《Insurance: Mathematics and Economics》、《ASTIN Bulletin》、《Scandinavian Actuarial Journal》、《中国科学》等国内外重要期刊 上发表论文三十余篇。