A Tail Dependent Risk Model With Random Weighting And The Ruin Probability

The classical risk model is usually consider without the effect of the interest force, but the interest force is an important factor for the insurance company in actual eco-nomic environment. At the same time, in the classical risk model, the claim amounts and the claim times are always assumed to be independent. But in practical con-text, this assumption can be restrictive. So more and more risk models with claims-dependent claim sizes have been studied. This paper considers the discrete time risk model of under random interest rate and dependent risks, and get a expression of the ruin probability. So, in this paper, we studied the problem of the ruin probability of Heavy-tailed dependent with random weights.This paper is divided into five chapters according in contents:In Chapter1, we mainly introduce the importance of the research to the question. Expounds the significance of the product of independent random variables in our real lives and some recent results and status. And gives the main problem of this paper, the ruin probability of random weighted sums and its maximumIn Chapter2, we introduce the definition of heavy-tailed distribution, some impor-tant distribution groups and the relation among of them. Also introduce an important property of the D family.In Chapter3, we introduce several lemmas and three theorems, Also obtained two corollaries, (a)If then have(b)If F∈R-α,0<α<∞, then haveIn Chapter4, we given the proof of the three theorems.In Chapter5, we give the discrete time risk model Also introduce the claim amount distribution belong for D family with stochastic in-terest rate and get the progressive expression of the ruin probability with the amount claimed which is pairwise asymptotic independence risk model, for any n=1,2,…, and...