Ruin Probability For The Generalized Double Non Homogeneous Poisson Risk Model

Risk theory, as a part of insurance or actuarial mathematics , deals with stochastic models of an insurance business and studies the probability of ruin .The classical compound Poisson risk model is one of principal models. In such a model the company receives a certain numbers of policies, which every policy has the same premiums.But in fact, the numbers of policy the company received during the different unit time are different. Based on this fact, the classical compound Poisson risk model to a new risk model R_t =u + c M(t)-S(t)are generalized, which the arrival of policies is non homogeneous Poisson process and the occurrence of claims is generalized non homogeneous Poisson process. We transform this model to a general double non homogeneous. Based on this model, an upper bound of the ruin probability is obtained and an explicit expression of ψ(u) is given when the arrival of policies and the occurrence of the claims have the same intensity function.