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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (3): 512-528.doi: 10.3969/j.issn.1005-3085.2026.03.009cstr: 32411.14.cjem.CN61-1269/O1.2026.03.009

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基于索赔信息不对称的主从随机微分再保险博弈

杨  鹏,   肖卫党   

  1. 西安财经大学数学学院，西安 710100
  • 收稿日期:2025-01-11 接受日期:2025-10-19 出版日期:2026-04-15 发布日期:2026-08-15
  • 基金资助:
    教育部人文社会科学研究一般项目(24YJAZH193)；陕西省自然科学基础研究计划(2025JC-YBMS-080).

Leader-follower Stochastic Differential Reinsurance Game Based on Asymmetric Claim Information

YANG Peng,  XIAO Weidang   

  1. School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100
  • Received:2025-01-11 Accepted:2025-10-19 Online:2026-04-15 Published:2026-08-15
  • Supported by:
    The Humanities and Social Sciences Project of the Ministry of Education of China (24YJAZH193); the Natural Science Basic Research Program of Shaanxi (2025JC-YBMS-080).

摘要：

从内部信息、信念异质和索赔信息学习三方面量化索赔信息不对称问题，进而研究再保险合同制定问题。通过域流扩张理论，引入保险人掌握索赔内部信息。通过在不同的概率分布下定义保险人和再保险人索赔额的分布和索赔发生次数的强度，引入保险人与再保险人信念异质。通过贝叶斯学习，引入再保险人关于索赔信息学习。以期望效用最大化准则为目标，给出保险人和再保险人的主从随机微分博弈问题。通过随机控制理论，求解主从随机微分博弈问题，得到保险人的最优索赔风险分担策略和再保险人的最优再保费定价策略，从而给出最优再保险合同。最后，从理论视角探究所得结果的保险和经济意义，研究结果可以较好地指导实际中的再保险。

关键词: 内部信息, 信念异质, 贝叶斯学习, 再保险, 随机控制

Abstract:

This paper quantifies the asymmetry claim information from three aspects: inside information, belief heterogeneity and claim information learning, and then studies the formulation of reinsurance contract. Through the theory of filtration expansion, the insurer is introduced to grasp the inside information of claims. By defining the distribution of claim amount and the intensity of claim occurrence for the insurer and the reinsurer under different probability distributions, the belief heterogeneity between the insurer and the reinsurer is introduced. Through Bayesian learning, this paper introduces the reinsurer's learning about claim information. Taking maximize the expected exponential utility criterion as the goal, the leader-follower stochastic differential game problem between the insurer and the reinsurer is given. Through stochastic control theory, the leader-follower stochastic differential game problem is solved, and the insurer's optimal claim risk sharing strategy and the reinsurer's optimal reinsurance pricing strategy are obtained, thus the optimal reinsurance contract is given. Finally, the  insurance and economic significance of the obtained results is explored from the theoretical perspective, and the research results can better guide reinsurance in practice.

Key words: inside information, belief heterogeneity, Bayesian learning, reinsurance, stochastic control

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