河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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投资-混合再保险模型下绝对破产概率最小化

（天津师范大学数学科学学院，天津 300387)
DOI： 10.13763/j.cnki.jhebnu.nse.202201014

Minimization of Absolute Ruin Probability Under Investment and Mixed-claim Reinsurance Model

CAO Qi,WANG Xiulian

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摘要/Abstract

摘要：

考虑投资-混合再保险的扩散渐近模型，在现有破产概念的基础上，定义了新的绝对破产的概念，将绝对破产概率定义为所要研究的值函数，推导出值函数对应的HJB(Hamilton-Jacob-Bellman)方程，通过控制区域，分别进行求解，得到投资、再保险的最优策略，进而得出最优值函数的显示解.最后，通过数值分析探讨了在最优策略下比例再保险对超额索赔再保险的影响.

Abstract：

Considering a diffusion approximation model for the risk model with investment and mixed-claim reinsurance, a new concept of absolute ruin probability is defined under the existing concept of ruin probability. The absolute ruin probability is defined as the value function to be studied, and the corresponding HJB(Hamilton-Jacob-Bellman)equation is derived. By distinguishing the control areas and solving equation separately, the optimal strategy of investment and reinsurance is derived and the explicit expression of the optimal value function is obtained. Furthermore, the effect of proportional reinsurance on excess-claim reinsurance under optimal strategy is discussed by numerical analysis.

关键词

关键词： 混合再保险； Hamilton-Jacob-Bellman方程；绝对破产概率；扩散渐近模型

Key words： mixed-claim reinsurance ; Hamilton-Jacob-Bellman equation ; absolute ruin probability ; diffusion approximation model

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