Acta mathematica scientia, Series B >
DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL
Received date: 2007-11-10
Revised date: 2008-05-16
Online published: 2010-07-20
Supported by
Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China
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.
MA Xue-Min , YUAN Hai-Li , HU Yi-Jun . DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1167 -1173 . DOI: 10.1016/S0252-9602(10)60114-2
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