Some Researches On Randomly Weighted Sums

There are some uncertain phenomena in the real world.Behind these uncertainties,there is usually some kinds of certain probability rule.Randomly weighted sums model based on probability and mathematical statistics is one of the most effective tools for solving such problems.Randomly weighted sums model can be applied to solve insurance risk problems and finance risk problems.In addition,it is related to extreme value theory,queuing theory and communications.In the past studies,people mainly studied the asymptotic formula of randomly weighted sums and their maxima.However,in the real world,n can also be a random variable in the randomly weighted sums model.This thesis studies the asymptotic formula of the tail probability of stochastic weighted sums and constructs a new asymptotic formula under the heavy-tailed distribution.This thesis mainly studies the content:1.This thesis studies the randomly weighted sums model under discrete-time conditions and establishes a new asymptotic formula.This asymptotic formula is established when n is a random variable in randomly weighted sums model,then we prove the asymptotic formula strictly.2.Using the characteristics of asymptotic formula constructed in the randomly weighted sums model,Monte Carlo simulations were used to perform numerical simulations of the asymptotic formula presented.The experimental results further prove the rationality of the asymptotic formula.From the experimental results,we can see that the asymptotic formula is reasonable.