Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (4): 998-1006.doi: 10.1016/S0252-9602(13)60058-2

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RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

 YANG Hu, XUE Kai*   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2012-05-29 Revised:2012-09-14 Online:2013-07-20 Published:2013-07-20
  • Contact: XUE Kai,xk canghai@163.com E-mail:yh@cqu.edu.cn; xk canghai@163.com
  • Supported by:

    This research was supported by the National Natural Science Foundation of China (11101451) and Ph.D. Programs Foundation of Ministry of Education of China (20110191110033).

Abstract:

In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims, in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Key words: semi-Markov risk model, constant interest force, asymptotic behaviors, heavy-tailed distributions

CLC Number: 

  • 62H15
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