Research On The Asymptotic Properties Of Two Types Of Insurance Financial Models

Using mathematical models to solve financial problems has become the basic method for modern economists to study the financial field,and the core of financial problems is risk management.Therefore,it has become the core of modern financial management to measure and reduce risks by constantly developing and optimizing financial mathematical models.The main research content of this paper is the asymptotic properties of two kinds of financial models.We first introduce the research status of the two financial theoretical models,namely,compound poisson risk process and entropic risk measure,and their asymptotic properties.Then,the two models are generalized,and two generalized models are obtained,namely,the constant interest force perturbation compound poisson risk model and the two kinds of entropic risk measure under normal condition.Because large deviations can effectively characterize rare events,they play an important role in the field of risk quantitative assessment,we put the core of this article through after the large deviation research extension of more detailed part of the two models on the asymptotic properties of the constant interest force disturbance in the process of the compound poisson risk claims the gap with the discounted value of the net present value of the asymptotic results and normal circumstances of two kinds of entropic risk measure to estimate asymptotic properties.This paper is divided into the following chapters.The first chapter introduces the research status of the two financial models and their asymptotic properties respectively.The second chapter mainly introduces the basic knowledge related to this paper.Basic concepts and important theorems are given here,including possion's shot noise process,large deviation theory,moderate deviation theory,the definition of relative entropy,the concept of entropic risk measure,and the introduction of Delta method.In chapter 3.we study the time value of the claim process in the constant interest force perturbation compound poisson risk in detail.The time value here is mainly described by the asymptotic results of the difference between the discounted value of the total claim and the net present value by study:ng the large deviations and moderate deviations In addit(?)n.at the end of the chapter,when the random variable obeys the exponential distribution,the large deviation and the moderate deviation of the difference between the total claim discount value and the net present value in the process of compound poisson risk with constant interest force perturbation are given,and the results are verified by simulation examples.In the fourth chapter,we first give the definition of the estimator of the convex entropic risk measure and the coherent entropy risk measure under normal conditions,and study some asymptotic properties of the estimator.It mainly including the normal situations of two kinds of entropic risk measure to estimate the consistency,large deviation,the moderate deviation and asymptotic normality,and the asymptotic properties of estimators gives two kinds of entropic risk measure under normal circumstances estimate interval estimation,the final use simulation to verify the result of interval estimation.The fifth chapter is the summary and reflection of the research content.