WANG Han-xing, YAN Yun-zhi, ZHAO Fei, FANG Da-fan. Markovian Risk Process[J]. Applied Mathematics and Mechanics, 2007, 28(7): 853-860.
Citation: WANG Han-xing, YAN Yun-zhi, ZHAO Fei, FANG Da-fan. Markovian Risk Process[J]. Applied Mathematics and Mechanics, 2007, 28(7): 853-860.

Markovian Risk Process

  • Received Date: 2006-11-07
  • Rev Recd Date: 2007-04-26
  • Publish Date: 2007-07-15
  • A Markovian risk process is considered, which is the generalization of the classical risk model. It is proper that a risk process with large claims is modelled as the Markovian risk model. In such a model, the occurrence of claims was described by a point process with it being the number of jumps for a Markov jump process from time 0 to t. The ruin probability of a company facing such a risk model was mainly studied. An integral equation satisfied by the ruin probability was obtained and the bounds for the convergence rate of the ruin probability are given by using a generalized renewal technique.
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  • [1]
    Grandell J.Aspects of Risk Theory[M].New York: Springer-Verlag,1991.
    [2]
    Gerber H U.An Introduction to Mathematical Risk Theory[M].S S Heubner Foundation Monograph series 8, Philadelphia,1979.
    [3]
    Mikosch T.Heavy-tailed modelling in insurance[J].Stochastic Models,1997,13(4):799-816. doi: 10.1080/15326349708807452
    [4]
    Klüppelbery C,Mikosch T.Large deviations of heavy-tailed random sums with applications in insurance and finance[J].J Appl Prob,1997,34(2):293-308. doi: 10.2307/3215371
    [5]
    WANG Hang-xing,FANG Da-fan,TANG Mao-ning.Ruin probabilities under a markovian risk model[J].Acta Mathematicae Applicatae Sinica, English Series,2003,19(4):621-630.
    [6]
    Asmussen S.Applied Probability and Queues[M].New York:John Wiley & Sons, 1987.
    [7]
    Asmussen S. Risk theory in a Markovian environment[J].Scand Act J,1989,69-100.
    [8]
    Wang Y H.Bounds for the ruin probability under a Markovian modulated risk model[J].Stochastic Models,1999,15(1):125-136. doi: 10.1080/15326349908807529
    [9]
    Blaszczyszyn B,Rolski T.Expansions for Markov-modulated systems and approximations of ruin probability[J].J Appl Prob,1996,33:57-70. doi: 10.2307/3215264
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