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山东大学学报(理学版)

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均值-方差标准下带跳的保险公司投资与再保险策略

孟祥波1,张立东1,杜子平2   

  1. 1.天津科技大学理学院, 天津 300457; 2. 天津科技大学经济与管理学院, 天津 300222
  • 收稿日期:2013-08-19 出版日期:2014-05-20 发布日期:2014-06-04
  • 作者简介:孟祥波(1981- ),男,硕士,讲师,研究方向为随机控制理论、金融数学.Email:mengxiangbo-1981@126.com
  • 基金资助:
    国家自然科学基金资助项目(71071111);教育部人文社会科学研究基金一般项目(11YJC910007);天津科技大学科学研究基金项目(20120110)

Investment and reinsurance strategy for insurers under #br# mean-variance criterion with jumps#br#

MENG Xiang-bo1, ZHANG Li-dong1, DU Zi-ping2   

  1. 1. College of Science, Tianjin University of Science & Technology, Tianjin 300457, China;
    2. College of Economics & Management, Tianjin University of Science & Technology, Tianjin 300222, China
  • Received:2013-08-19 Online:2014-05-20 Published:2014-06-04

摘要: 研究了均值-方差标准下保险公司面临的投资与再保险最优策略问题,其盈余过程受控于一个跳-扩散模型,目的是寻找相应的时间相容性策略。假定金融市场由一个无风险资产和多个服从几何Levy过程的风险资产组成,通过求解广义HJB方程,得到了最优时间相容性投资和再保险策略的解析表达式以及最优值函数。

关键词: 投资与再保险, 时间相容性策略, 均值-方差标准, 多种风险资产, 广义HJB方程

Abstract: An optimal investment and reinsurance problem for insurers under mean-variance criterion was investigated, whose surplus process is described by a more general jump-diffusion process and aims to seek the corresponding time-consistent strategy. The financial market consists of one risk-free asset and multiple risky assets whose price processes follow geometric Levy processes. The closed-form expressions for the time-consistent investment and reinsurance strategies and the optimal value function were derived by solving an extended Hamilton-Jacobi-Bellman equation.

Key words: investment and reinsurance, multiple risky assets, extended Hamilton-Jacobi-Bellman equation, time-consistent strategy, mean-variance criterion

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