数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (2): 333-340.doi: 10.1016/S0252-9602(13)60002-8

• 论文 • 上一篇    下一篇

DOUBLE-MARKOV RISK MODEL

莫晓云|周杰明|欧辉|杨向群*   

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China;Hunan University of Finance and Economics, Changsha 410205, China; College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Education Ministry of China), Hunan Normal University, Changsha 410081, China
  • 收稿日期:2011-11-09 修回日期:2012-05-17 出版日期:2013-03-20 发布日期:2013-03-20
  • 通讯作者: 杨向群|xqyang@hunnu.edu.cn E-mail:moxyun72@163.com; zhjm04101@126.com; bt huiou@sina.com; xqyang@hunnu.edu.cn
  • 基金资助:

    This work is supported by NSFC (11171101, 11271121), Doctoral Fund of Education Ministry of China (20104306110001), and Scientific Research Fund of Hunan Provin-cial Education Department (12C0562).

DOUBLE-MARKOV RISK MODEL

 MO Xiao-Yun, ZHOU Jie-Ming, OU Hui, YANG Xiang-Qun*   

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China;Hunan University of Finance and Economics, Changsha 410205, China; College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Education Ministry of China), Hunan Normal University, Changsha 410081, China
  • Received:2011-11-09 Revised:2012-05-17 Online:2013-03-20 Published:2013-03-20
  • Contact: YANG Xiang-Qun|xqyang@hunnu.edu.cn E-mail:moxyun72@163.com; zhjm04101@126.com; bt huiou@sina.com; xqyang@hunnu.edu.cn
  • Supported by:

    This work is supported by NSFC (11171101, 11271121), Doctoral Fund of Education Ministry of China (20104306110001), and Scientific Research Fund of Hunan Provin-cial Education Department (12C0562).

摘要:

Given a new Double-Markov risk model DM = (μ, Qν, H; Y, Z) and Double-Markov risk process U = {U(t), t ≥ 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.

关键词: Q process, Markov chain, Double-Markov risk characterization, survival prob-ability, recursion formula

Abstract:

Given a new Double-Markov risk model DM = (μ, Qν, H; Y, Z) and Double-Markov risk process U = {U(t), t ≥ 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.

Key words: Q process, Markov chain, Double-Markov risk characterization, survival prob-ability, recursion formula

中图分类号: 

  • 60J27