Asymptotic Analysis For Tails Of The Moments For Random Sums With Dominated Variation

Insurance risk measurement is an important issue in the field of insurance risk.Common risk measurement indicators include ruin probability,Conditional Tail Expectation(CTE),and Value at Risk(VaR).The essence of these indicators is tails of probability and moment of the total claim amount.On the other hand,the classical risk model assumes that the claims amount are independent of each other and follow the light-tailed distribution,but many studies have found that insurance companies' claims,venture capital asset value,and major disaster losses do not meet the light-tailed and mutual independent assumptions,but have Heavy-tailed distribution of correlations.Therefore,in order to accurately describe insurance risks,more and more scholars have begun to study the nature of heavy tailed risk models and tails of probability of risks in the context of dependency structure.Under the assumption of quasi-asymptotically independent dominated varying tailed distributions,this thesis studies the asymptotic behavior of tails of higher-order moment of random weighted sums of random variable sequences.The thesis studies the asymptotic behavior of tails of moment of the randomly weighted sum and its maximum value of random variable sequences which belonging to the long tailed distribution class and dominated varying tailed distribution class under the weakly dependent structure,defines a dependent structure which is weaker than pairwise strongly quasi asymptotically independent and add a moment condition to the weighted term,obtains tails of moment of sum of random variables asymptotic equivalence of the sum of tail of moment of random variables.Secondly,the sequence of quasi asymptotically independent random variables in the dominated varying tailed distribution class is considered,and the upper and lower bounds of the maximum of the random weighted sum of infinite terms are obtained.Then,extends the condition to the dominated varying tailed distribution class and pairwise quasi-asymptotically independent random variable sequence on the basis of the second chapter,studies tails of moment of random sum of random variable,and obtains a convenient upper and lower bound.Finally,The thesis considers the discrete time heavy tailed risk model,and puts the main conclusions in the context of insurance risk for application examples,and use the main results to obtain the asymptotic formula of the ruin probability in the discrete dependent model with interest rate and satisfying the unilateral linear structure.