| 引用本文: | 曾燕,李仲飞.风险资本约束下保险公司的最优比例再保险–投资策略[J].控制理论与应用,2011,28(4):467~471.[点击复制] |
| ZENG Yan,LI Zhong-fei.Optimal proportional reinsurance-investment policies for an insurer under Capital-at-Risk constraint[J].Control Theory and Technology,2011,28(4):467~471.[点击复制] |
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| 风险资本约束下保险公司的最优比例再保险–投资策略 |
| Optimal proportional reinsurance-investment policies for an insurer under Capital-at-Risk constraint |
| 摘要点击 2750 全文点击 2249 投稿时间：2010-01-07 修订日期：2010-06-18 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.4.CCTA100026 |
| 2011,28(4):467-471 |
| 中文关键词 风险资本约束 比例再保险策略 投资策略 保险公司 整体风险 |
| 英文关键词 Capital-at-Risk constraint proportional reinsurance policy investment policy insurer integral risk |
| 基金项目 国家杰出青年科学基金资助项目(70825002). |
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| 中文摘要 |
| 本文研究保险公司的再保险–投资问题. 假定保险公司的整体风险由风险资本(Capital-at-Risk, CaR)来度量; 盈余过程由扩散模型近似表示; 在任意时刻保险公司可购买比例再保险(或获取新业务)和投资无风险资产与多种风险资产; 风险资产的价格由几何布朗运动驱动. 保险公司的目标是在整体风险CaR受约束的条件下最大化终端财富的期望值. 对这一问题, 建立了两个均值--CaR模型. 利用分层优化方法和变分法, 得到了模型的最优比例再保险–投资策略以及有效边界的解析表达式. |
| 英文摘要 |
| This paper investigates a reinsurance-investment problem for an insurer. Assume that the integral risk of the insurer is measured by Capital-at-Risk(CaR), the surplus process is described by a diffusion approximation model; the insurer is allowed to purchase proportional reinsurance(or acquire new business) and to invest on a risk-free asset and multiple risky assets at any time; the prices of risky assets are driven by the model of geometric Brownian motions. The target of the insurer is to maximize the expectation of the terminal wealth under a CaR constraint. Two mean-CaR models are established for the problem. Explicit expressions of the optimal policies and efficient frontiers to the models are derived by using a hierarchical optimization method and the variational calculus approach. |