Asymptotic Estimate For The Finite-time Ruin Probability Of Multi-risk Perturbed Model

As we know risk theory has a long history of more than one hundred years, the ruin theory is an important part of it, which has already developed into a subject. We usually use mathematical models to describe and study the risks which is faced by insurance companies in ruin theory, and many researchers have made a lot of achievements and constructed classical models.We propose a multi-risk model based on the classical risk models and improve this model in this paper. For the case that{Ni(t),t≥0},i=1,2,...k are common renewal counting processes, the asymptotic estimate for the finite-time ruin probability based on Tsum, were derived. And we also derive the asymptotic estimate for the finite-time ruin probability of two policy subtraction under other assumptions. Besides we consider the case that the{Ni(t),t≥0},i=1,2,...k are dependent Poisson processes, and we obtain the asymptotic estimate for the finite-time ruin probability based on Tmax.