稀疏相依风险模型下具有时滞效应的最优再保险和投资问题
Optimal Reinsurance and Investment Problems with Delay Effects in a Thinning Dependent Risk Model
摘要: 假设保险公司有两种不同的保险业务，它们之间存在着稀疏相依的关系，保险公司在购买比例再保险的同时将盈余部分投资于无风险资产和风险资产，其中通过不变方差弹性模型刻画出风险资产的价格过程，进一步考虑时滞效应的影响，在均值–方差准则下建立最优控制问题，利用随机控制理论得到相应的HJB方程，然后得到最优的再保险和投资策略，并分析模型参数对最优策略的影响。
Abstract: Assuming that the insurance company has two different insurance businesses, which have sparse dependencies between them, while purchasing proportional reinsurance, the insurance company invests the surplus in risk-free assets and risky assets. Among them, the price process of risky assets is described by the CEV model, and the impact of time delay is further considered. Under the mean-variance criterion, an optimal control problem is established, and the corresponding HJB equation is obtained using stochastic control theory. Then the optimal reinsurance and investment strategies are obtained, and the impact of model parameters on the optimal strategy is analyzed.
文章引用：高钰杰, 张强. 稀疏相依风险模型下具有时滞效应的最优再保险和投资问题[J]. 应用数学进展, 2024, 13(4): 1523-1535. https://doi.org/10.12677/aam.2024.134143

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