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This mansuscript focuses on a kind of two-dimensional
risk model with stochastic premium income and the model allows for dependence
between premiums and claims. By Laplace transforms, we prove that the model
proposed in this paper can be reduced into a kind of risk model with stochastic
premium incomes, and the premium income is independent of the claim process.
When the individual claims are the "light-tailed" case, an upper bound for
ruin probability is derived by martingale approach. When the claims belong to
a kind of heavy-tailed distribution, the asymptotic estimation for ruin
probability is given when the initial surplus tends to infinity.