Ruin Probability for a Markovian Risk Model with Two-type Claims

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 ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

• Dongdong Zhang
• Deran Zhang

• Risk model
• ruin probability
• Markov jump process
• integral equation.

[1] Asmussen S. Risk theory in a Markovian environment. Scand Actuarial
J, 1989, 66-100.
[2] Blaszczyszyn B, Rolski T. Expansions for Markov-modulated systems
and approximations of ruin probability. J appl Prob, 1996, 33:57-70.
[3] Cramer H. On the mathematical Theory of risk. Skandia Jubilee Volume,
Stockholm, 1930.
[4] Helena Jasiulewicz, Probability of ruin with variable premium rate in a
Markovina environment. Insurance: Mathematics and Economics 2001;
29: 291-296.
[5] Li S, Garrido J. Ruin probabilities for two classes of risk processes.
ASTIN Bulletin 2005; 35: 61-77.
[6] Li S, Lu Y. On the expected discounted penalty functions for two classes
of risk processes. Insurance: Mathematics and Economics 2005; 36: 179-
193.
[7] Wang H.X. Yan Y.Z. et al. Markovian risk process. Applied Mathematics
and mechanics(English edition), 2007,28(7):955-962.
[8] Yang H, Zhang Z. On a class of renewal risk model with random
income. Applied Stochastic Models in Business and Industry 2009; 25(6):
678¨C695.
[9] Yuen K.C., Guo J., Wu X. On a correlated aggragate claims model
with Poisson and Erlang risk processes, Insurance: Mathematics and
Economics 2002; 31: 205-214.