Study On The Actuarial Present Value Of The Dual Random Four-element Life Insurance

Since the opening and opening up of two children,the importance of the research on the four-element family joint insurance has been greatly improved.The research in this field can also effectively improve the rationality of the pricing of multielement insurance products.The research object of this paper is the four-element family joint insurance under the assumption of doubly stochastic,stochastic interest rate in this paper is geometric Brownian motion with a constant shift,random death is obtained by combining the experience life table of Chinese insurance industry(2010-2013)and Markov chain.The main content of the first chapter is the research background,research status,research methods and significance of this paper;the second chapter introduces the preparation knowledge of this paper,including interest rate theory,the theory of interest annuity and death force,and this chapter also introduces the life table,the joint life insurance and annuity which are mainly discussed in the later chapters;the third chapter introduces two kinds of stochastic processes used in this paper,the geometric Brownian motion and Markov chain,and gives the Markov chain matrix under the assumption of four-element;the main work of the fourth chapter is the construction of four-element joint distribution,and the deduction of expressions of actuarial present values of four-element joint life insurance and annuity under assumptions of constant force of death and interest.The fifth chapter is the first important chapter in this paper.The main content of this chapter is to deduce the actuarial present value expression of four-element joint life insurance and annuity under the single stochastic hypotheses which death follows Markov chain and interest rate follows geometric Brown motion respectively.Then we combine the experience life table of Chinese life insurance industry and Markov chain,and construct the doubly stochastic actuarial model with interest rate under geometric Brown motion,then calculate actuarial present value.In the end,several parameters which affect the actuarial present value have been analyzed.The last chapter of this paper is the second important chapters.In this chapter,we simulated the doubly stochastic four-element joint life actuarial model which is obtained in chapter five by numerical method,and we find that the actuarial model similar to F distribution,then checks the consistency of the F distribution.