Research On Ruin Probability With Investment Strategy

The risk model is a stochastic model about the surplus of the insurance company's funds.It is the theoretical basis of the insurance company's operation and management.For a long time,as the level of research on the classic bankruptcy theory model and corresponding classic conclusions has continued to deepen,the field of research has continued to expand.However,the classical bankruptcy model is a theoretical study of the “small claims” situation.The study of the probability of bankruptcy in the “big claims” case,more precisely,the study of the heavy-tailed distributed bankruptcy theories must find new ways to use new tools.At present,the study of the heavy tail distribution mainly focuses on two aspects: on the one hand,it is to find ways to establish the tail asymptotic equivalence relations of ruin probability;on the other hand,it is based on the tail asymptotic equivalence relations to find a way to establish partial equivalence relations.As the form of investment becomes more and more complex,it becomes more and more necessary to reflect the investment strategy into the model.At the same time,the dependency structure of insurance products is also reflected in the risk model,which is equally important.This article is based on the classic risk model and reference scholars research results based on the consideration of insurance companies to invest their own insurance funds in a single risk assets and gain investment income.In this paper,under the premise that the claim arrival process is the update counting process,and the claim amount obeys the heavy-tailed distribution,the asymptotic expression of the ruin probability is obtained,which expands the previous research results.The main contribution of this paper lies in three aspects:(1)Focusing on investment strategy,considering adjusting the ratio of venture capital investment and riskless investment,establishing a discrete risk model with discount function having a general function and investment strategy.(2)In examining the amount of compensation and the stochastic discount factor,there is a dependent relationship,a discrete-time investment risk model with a dependent structure is established,and the asymptotic expression of the corresponding infinite-time ruin probability is studied,and the relevant results are simulated.(3)Based on the updated risk model,focusing on examining the relationship between the amount of the claim and the arrival time interval of the claim,and the stochastic discount factor has a general function form,establish acontinuous-time investment risk model with a dependent structure,and further conclude that it has general The conditions under which the random discount factor in the form of a function satisfies the condition and the progressive expression of the ruin probability under the corresponding model.The following is a brief description of the above results:1.Considering that the distribution of claim amounts belongs to heavy-tailed distribution families,and that the sequence of claim amounts and stochastic discount factors have a discrete-time risk model with dependent structures,the asymptotic expression of the corresponding final ruin probability is studied,and the ruin probability of the model is simulated.2.Under the premise that the claim amount sequence obeys the heavy-tailed distribution,consider that the claim amount sequence and the claim arrival time interval have a dependent structure,and the stochastic discount factor is a function of the time t and the investment strategy ? having a general form,construct a model.The conditions of random discount factor satisfaction and the asymptotic expression of the ruin probability of continuous-time risk model are studied.