Efficient Monte Carlo Simulation Of Actuarial Multi-State Model For Life Insurance

Since the reform and opening up,with the continuous development of my country’s financial market,the people’s demand for economic security has grown day by day,which has promoted the vigorous development of my country’s insurance industry.Life insurance is an insurance commodity based on social insurance with the underwriter’s life distribution as the core.The research on the actuarial numerical method of life insurance has important financial theory and practical application value.The multi-state model is based on the stochastic process in probability mathematics,which can intuitively express the transformation process between different life states and states in the life insurance business.Its application advantage in the continuous-time discrete state scenario brings the possibility of the application of the multi-state model in life insurance actuarial.By summarizing the previous research methods and results on life insurance actuarial,this paper uses two more efficient Monte Carlo(MC)methods-quasi monte carlo(QMC)and Markov Chain Monte Carlo(MCMC)to conduct numeric value simulation research on the actuarial multi-state model of life insurance.The numeric value experiment part mainly selects the permanent disability model in the actuarial multi-state model of life insurance,takes a 10-year term life insurance contract as an instance to construct a specific life insurance environment,and conducts QMC and MCMC numeric value simulation on the mortality parameters of the Thiele differential equation of the liability reserve.Through the simulation results,the liability reserve is calculated by the iterative method,which is compared with its Thiele differential equation numeric value solution.The results show that the numeric value simulation using QMC and MCMC methods is carried out when the underwriter is in state 0,that is,in the case of a healthy state The simulation efficiencies of the liability reserve are 82.64%and 80.27%respectively,and the simulation efficiencies of the liability reserve in the case of state 1,that is,disease state,are 89.05%and 90.32%respectively.The simulation effect is good,which verifies the high-efficiency monte carlo method in life insurance actuarial applicability and superiority.