Abstract
In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force. We obtain the upper bound and Lundberg-Cramér approximation for the infinite-time ruin probability, and consider the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed. We show that the model in our paper has similar results to the classical risk process and some existing generalized models.
Highlights
In the classical non-life insurance risk model, the Lundberg-Cramér surplus process has the form N (t)U (t) = u + ct – Yi, ( . ) i=where u ≥ is the initial capital of an insurance company, c > is the rate of premium income, {N(t), t ≥ }, which represents the total numbers of claims up to time t, is a homogeneous Poisson process with intensity λ, Yi describes the amount of the ith claim, and {Yi, i ≥ } is a sequence of nonnegative independent and identically distributed random variables, which is independent of N(t)
Where u ≥ is the initial capital of an insurance company, c > is the rate of premium income, {N(t), t ≥ }, which represents the total numbers of claims up to time t, is a homogeneous Poisson process with intensity λ, Yi describes the amount of the ith claim, and {Yi, i ≥ } is a sequence of nonnegative independent and identically distributed random variables, which is independent of N(t)
Many papers assume that the premium income is no longer a linear function of time t
Summary
Boikov [ ] generalized the classical risk model to the case where the premium was modeled as another compound Poisson process, he derived the integral equations and exponential bounds for non-ruin probability. We consider a perturbed risk model with stochastic premiums and constant interest force t t In the rest of this paper, we consider the upper bounds and the Lundberg-Cramér approximation for the infinite-time ruin probability, and we obtain the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed.
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