Lundberg's Inequality of Erlang(2) Perturbed Risk Model in Markovian Environment

A famous problem in nonlife actuarial field is considered in this paper. We extend Erlang(2) perturbed risk model to a Markov dependent model in which the inter-claim time, the claim amount, the premium rate and the volatility of the diffusion process are all regulated by a continuous-time Markov process. By the means of the martingale approach, we obtain an upper bound of the ruin probability of our model, described as the Lundberg's inequality, and derive a representation for the corresponding adjustment coefficient.