保险模型中的 Stackelberg 博弈

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保险模型中的 Stackelberg 博弈
Stackelberg Game in Insurance Models

DOI: 10.12677/AAM.2024.135230, PDF, 下载: 19 浏览: 43 科研立项经费支持
作者: 孙少迪, 梁晓青^*：河北工业大学理学院，天津
关键词: Stackelberg 博弈；效用准则；风险度量；近似解；Stackelberg Game； Utility Criteria； Risk Measure； Approximate Solution

摘要: 本文研究保险问题中的单期 Stackelberg 博弈的均衡解。假设再保险公司的保费原则是 Π(R) = E[P (X − R)]，本文使用的目标函数包括最小化风险的凸度量，最大化期末财富的预期效用，最大化期末财富的二次效用。通过对变量函数进行 Taylor 展开，得到保险公司留存函数以及再保费价格的最优近似解。

Abstract: We consider the equilibrium solution to the single-period Stackelberg game in the insurance problem. Assuming that the premium principle is Π(R) = E[P (X − R)], we use objective functions that include minimizing the convex measure of risk, maximiz- ing the expected utility of terminal wealth, and maximizing the quadratic utility of terminal wealth. By applying Taylor expansions to the variables, we obtain optimal approximate solutions for the insurer retention function as well as the premium price.

文章引用：孙少迪, 梁晓青. 保险模型中的 Stackelberg 博弈[J]. 应用数学进展, 2024, 13(5): 2424-2435. https://doi.org/10.12677/AAM.2024.135230

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