DOUBLE-MARKOV RISK MODEL

doi:10.1016/S0252-9602(13)60002-8

Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (2): 333-340.doi: 10.1016/S0252-9602(13)60002-8

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DOUBLE-MARKOV RISK MODEL

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

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).

Abstract

Abstract:

Given a new Double-Markov risk model DM = (μ, Q, ν, 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

CLC Number:

60J27

MO Xiao-Yun, ZHOU Jie-Ming, OU Hui, YANG Xiang-Qun. DOUBLE-MARKOV RISK MODEL[J].Acta mathematica scientia,Series B, 2013, 33(2): 333-340.

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DOUBLE-MARKOV RISK MODEL

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