Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1167-1173.doi: 10.1016/S0252-9602(10)60114-2

• Articles • Previous Articles     Next Articles

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

 MA Xue-Min, YUAN Hai-Li, HU Yi-Jun   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan |430072, China
  • Received:2007-11-10 Revised:2008-05-16 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China

Abstract:

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of
exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Key words: Homogeneous Markov process, ruin probability, deficit, duration of negative surplus, compound Poisson risk model

CLC Number: 

  • 60J75
Trendmd