Research On Implicit Pension Debt Actuarial Models With Stochastic Interest Rate

In the context of global aging,pension issues gain much of national attention.Pension insurance has become one of the hot issues as a closely related topic.The establishment of pension insurance system of China in the early days has undergone several major changes.Our pension insurance system gradually became matured through significant reform.China begins partial funds system reform in its old-age insurance system-from “cash payment” to“social overall plan and individual account system”.Our old-age insurance problems in the system lead the debt to appear and gradually be dominant and showed a tendency of increasing each year.In such cases,determining the exact size of the implicit pension debt is particularly important.Firstly,the insured population was re-divided on the basis of the original data according to National document [1997] No.26 and National document [2005] No.38.Implicit pension debt actuarial models under fixed interest rate were established.The implicit pension debt of January 1,2013 was calculated.The sensitivity analysis to several factors such as interest rate and wage growth rate is conducted.The size of the implicit pension debt calculated provided a theoretical basis for relevant departments.Secondly,considering the impact of various factors on interest rate fluctuation,the function of interest force was built by adopting the Wiener process,reflecting Brownian motion,Gauss process,Poisson process and double stochastic process.Implicit pension debt actuarial models with stochastic interest rate were established and the expectation of implicit pension debt was given.Thirdly,Monte Carlo simulation was performed through numerical examples.Then the diagram of empirical distribution function and the diagram of empirical density function of the implicit pension debt with interest rate under Wiener process,reflecting Brownian motion and Gauss process were obtained.The result provided a theoretical basis to estimate the exact size of implicit pension debt for Chinese government.