Asymptotic Estimaties For Two Finite-time Ruin Probabilities In A Generalized Dependent Bidimensional Risk Model

In actuarial science and applied probability theory.ruin theory is a theory that uses mathematical models to describe the vulnerability of insurance companies to ruin.As the central core content of ruin theory.ruin probability is an important indicator in actuarial science to measure the adequacy and solvency of insurance products.Since Einbrechts et al.(1997)studied the problem of ruin probability in extreme events and introduced the definition and properties of the family of heavy-tailed distributions in detail.the empirical and theoretical research on heavy-tailed distributions in economics and finance has become more mature.An increasing number of actuaries have begun to study heavy-tailed insurance risk models.This paper is based on the classic insurance risk model.especially considering the assumption that each pair of claims obeys a specific dependence structure,and studies ruin probabilities of a generalized bidimensional risk model with dependent,and heavy-tailed claims and additional net loss process.Firstly,when the claim sizes have long-tailed and dominated-varving-tailed distributions.precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived.where the two claim-number processes from different lines of business are almost arbitrarily dependent.Secondly.under some extra conditions on the independence relation of claim inter-arrival times.we extend the class of the claim size distribution to the subexponential distribution class.Secondly,under some extra assumptions on the independence relation of claim inter-arrival times,we extend the class of the claim size distributions to the subexponential distribution class.Thirdly.we note the reason why the asymptotic expressions of ruin probability are different.When the claim arrival process of the two counting processes is the same,the asymptotic expression of the ruin probability is not in the form of directly replacing the estimated expression of in the theorem in Chapter 3 with the same counting process form.We also give a new lemma applicable to this situation and the asymptotic expression of the correct ruin probability.Finally,to verify the accuracy of the obtained theoretical result,under the example of the specific dependent structure in Chapter 2,simulation studies are performed via the Monte Carlo method.