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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (5): 49-57.doi: 10.6040/j.issn.1671-9352.0.2016.244

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现代风险模型的扩散逼近与最优投资

张节松   

  1. 淮北师范大学管理学院, 安徽 淮北 235000
  • 收稿日期:2016-06-07 出版日期:2017-05-20 发布日期:2017-05-15
  • 作者简介:张节松(1981— ), 男, 博士, 讲师, 研究方向为保险与金融风险管理.E-mail: j-s-zhang@126.com
  • 基金资助:
    安徽省自然科学基金资助项目(1608085QG169);安徽省高校优秀青年人才支持计划重点资助项目(gxyqZD2016104);安徽省高校自然科学研究一般项目(KJ2014B16)

Diffusion approximation and optimal investment for modern risk model

ZHANG Jie-song   

  1. School of Management, Huaibei Normal University, Huaibei 235000, Anhui, China
  • Received:2016-06-07 Online:2017-05-20 Published:2017-05-15

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摘要： 采用基于保单进入过程的现代风险模型刻画保险公司的盈余过程,利用鞅中心极限定理证明此类风险过程可逼近为具有时变漂移率的扩散过程。在此基础上,假定保险人购买固定比例再保险并投资Black-Scholes金融市场,研究了最小化破产概率的投资决策问题。运用动态规划原理,获得了最优策略以及值函数的显式表达式。

关键词: 保单进入过程, 最优投资, 扩散逼近, 鞅中心极限定理

Abstract: Based on the modern risk model based on the policy entry process, this paper describes the surplus process of the insurance company, and proves that the risk process can be approximated to the diffusion process with time-varying drift rate by using the martingale central limit theorem. On this basis, it is assumed that the insurers buy a fixed proportion of reinsurance and invest in the Black-Scholes financial market and study the investment decision-making problem that minimizes the probability of ruin. The explicit expression of the optimal strategy and the value function is obtained by using the dynamic programming principle.

Key words: policy entrance process, martingale central limit theorem, diffusion approximation, optimal investment

中图分类号: 

  • F840.32
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