{"title":"Ruin Probability for a Markovian Risk Model with Two-type Claims","authors":"Dongdong Zhang, Deran Zhang","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1860,"pagesEnd":1864,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8414","abstract":"<p>In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t &cedil; 0}, i = 1, 2, where {Ni(t), t &cedil; 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t &cedil; 0} . The ruin probability &ordf;(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability &ordf;(u) is obtained and the bounds for the convergence rate of the ruin probability &ordf;(u) are given by using key-renewal theorem.<\/p>\r\n","references":"[1] Asmussen S. Risk theory in a Markovian environment. Scand Actuarial\r\nJ, 1989, 66-100.\r\n[2] Blaszczyszyn B, Rolski T. Expansions for Markov-modulated systems\r\nand approximations of ruin probability. J appl Prob, 1996, 33:57-70.\r\n[3] Cramer H. On the mathematical Theory of risk. Skandia Jubilee Volume,\r\nStockholm, 1930.\r\n[4] Helena Jasiulewicz, Probability of ruin with variable premium rate in a\r\nMarkovina environment. Insurance: Mathematics and Economics 2001;\r\n29: 291-296.\r\n[5] Li S, Garrido J. Ruin probabilities for two classes of risk processes.\r\nASTIN Bulletin 2005; 35: 61-77.\r\n[6] Li S, Lu Y. On the expected discounted penalty functions for two classes\r\nof risk processes. Insurance: Mathematics and Economics 2005; 36: 179-\r\n193.\r\n[7] Wang H.X. Yan Y.Z. et al. Markovian risk process. Applied Mathematics\r\nand mechanics(English edition), 2007,28(7):955-962.\r\n[8] Yang H, Zhang Z. On a class of renewal risk model with random\r\nincome. Applied Stochastic Models in Business and Industry 2009; 25(6):\r\n678\u252c\u00bfC695.\r\n[9] Yuen K.C., Guo J., Wu X. On a correlated aggragate claims model\r\nwith Poisson and Erlang risk processes, Insurance: Mathematics and\r\nEconomics 2002; 31: 205-214.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}