Research On Survival Life Insurance Portfolio And Its Risk Based On Stochastic Return Rate Model And Optimal Copula Function

Under the condition of guaranteeing no ruin of an insurance company,we study the optimal dividend strategy and the investment portfolio of an insurance company when the dividend processes are Erlang(2)distributed and the rates of return are MA(q)modelled,respectively.Firstly,an index is introduced into the classical risk model,assuming that initial surplus or premiums are affected by time.Then we extend it into dividend processes,and when the processes of dividend are Erlang(2)distributerd,the corresponding integro-differential equations are obtained.By solving the equations,an implicit expression of the optimal strategy is obtained.The numerical simulation method is used to analysis the influence of different factors with changing the optimal strategy.Secondly,we extend this idea to the dual risk model.The optimal dividend before ruin is studied,and the optimal periodic barrier strategy is considered under the conditions of the dividend decision times are Erlang(2)distributed and income is linear on the dual risk model.In addition,th e figs between the optimal strategy and other economic factors in the model are described by numerical simulation and the corresponding economic explanations are gived.Finally,we study the life insurance p.ortfolio and its risk under MA(q)model.That is,when the rates of return follows the MA(q)processes,combined with the Copula model of the dependent mortality rate,the distribution function of the present value of expected loss random variable under a given pricing time is derived,and the GlueVaR risk measurement method is used to measure the risk of expected losses.We can help insurance companies to adjust and control risks,choose the risks they can bear based on different risk attitudes,and formulate measures to deal with risks in a timely manner.