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含不动产项目的保险公司再保险-投资策略

陈树敏1  郝志峰2,*   

  1. 1. 广东工业大学管理学院, 广州 510006;  2. 佛山科技学院, 广东佛山 528000
     
  • 收稿日期:2013-01-17 出版日期:2018-03-15 发布日期:2018-03-15
  • 通讯作者: 郝志峰 mazfhao@scut.edu.cn
  • 基金资助:

    国家自然科学基金(Nos. 71671047, 71721001,  71601055, 71501050, 71471045)

Optimal reinsurance-investment strategies for an insurance company with real estate investment 

CHEN Shumin1  HAO Zhifeng2,*   

  1. 1.  School of Management, Guangdong University of Technology, Guangzhou 510006, China; 2. Foshan University, Foshan 528000, Guangdong, China
  • Received:2013-01-17 Online:2018-03-15 Published:2018-03-15

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摘要：

站在保险公司管理者的角度, 考虑存在不动产项目投资机会时保险公司的再保险--投资策略问题. 假定保险公司可以投资于不动产项目、风险证券和无风险证券, 并通过比例再保险控制风险, 目标是最小化保险公司破产概率并求得相应最佳策略, 包括: 不动产项目投资时机、 再保险比例以及投资于风险证券的金额. 运用混合随机控制-最优停时方法, 得到最优值函数及最佳策略的显式解. 结果表明, 当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目. 进一步的数值算例分析表明: (a)~不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系, 收益率越高则投资阈值越低; (b)~市场环境较好(牛市)时项目的投资阈值降低; 反之, 当市场环境较差(熊市)时投资阈值提高.

关键词: 不动产项目, 风险投资, 比例再保险, 破产概率, 混合随机控制-最优停时问题

Abstract:

Standing at the viewpoint of the decision maker of an insurance company, this paper investigates the reinsurance-investment strategies for an insurance
company with option of real estate investment. We assume that the insurance company has the possibility of investing in one real project, which will cost the insurance company a fixed amount of wealth and will bring in a fixed income rate as return. The insurance company may also invest its wealth in a Black-Scholes financial market with one risk-free asset (bond, or bank account) and one risky asset (stock), and may reduce its risk exposure or increase its premium using proportional reinsurance contract. The insurance company's main objective is the minimal ruin probability and the corresponding optimal strategy (including the timing of real investment, proportion of reinsurance and the amount of money invested in risky asset). With methodology of combined stochastic
control and optimal stopping, we obtain the value function and the optimal strategy explicitly. Finally, we analyze the optimal strategy numerically to illustrate our results. It is shown that: (a) The investment threshold of real project is mainly affected by the project's return; its connection with the cost of the real investment is vague. A higher real ivestment return leads to a lower investment threshold. (b) The real investment threshold is lower in a bear market than that in a bull market.

Key words: real investment, risky-asset investment, proportional reinsurance, ruin probability, combined stochastic control and optimal stopping problem