Asymptotic Analysis Of Ruin Probabilities For Bidimensional Renewal Risk Models With Stochastic Interest Return

Ruin probability is one of the important subjects of actuarial mathematics and probability statistics,and also the core of risk theory.The bankruptcy theory can be traced back to the early 20th century,so far,there are two main research methods of ruin probabilities,renewal demonstration method and martingale method.In this paper,we focus on asymptotic analysis of the ruin probabilities of the two-dimensional risk model with stochastic investment return.Firstly,we make the following assumptions on the model,the insurance companies have two types of insurance,there claims are independent random variables and belong to the regular distribution family,the time arrive of claims are at the same.Simultaneously,Insurance companies can invest in risk-free assets and risky assets,the investment process is assumed to be a geometric levy process{eRt,t?0}.Under these assumptions,we obtain the asymptotic estimates of ruin probabilities for the two-dimensional risk model.Secondly,based on the assumptions of the previous chapter,we assume that the two types of claims are not independent.This dependency is characterized by the joint distribution function FGM,then we extend the first two ruin probabilities of the two-dimensional risk model with stochastic investment return.Based on the previous proofs,we use the method of moment estimation to calculate the parameters of investment process,geometric levy process {eRt,t?0}.According to the insurance datas of Ping An Property&Casualty,from 2011 to 2013,We use the maximum likelihood estimation and Kolmogorov test to fit and estimate the claims distribution of life insurance and non-life insurance.Finally,we substitute the distributions of the claim amount and the parameters of the geometric levy process into the asymptotic formula of the ruin probabilities,then calculate the asymptotic estimate values and make a simple portfolio analysis.