The Study On The Modeling And Simulation Of Individual Post-Retirement Financial Planning

The global life expectancy has been increasing since last five decades. The population aging trend has becoming a fact and the financial deficits of the governments have getting worse and worse both accelerate the current old-age economic protection system to be in crisis. The world Bank advanced to the extension of the multipillar model beyond the three-pillar structure to encompass as many as five pillars, extend to family support and individual saving account, for old-age, but the family structure has been changing to fall fertility rates which makes family support to be useless. Hence, preparing the individual retirement financial planning is the only way to do and the best policy to make. Before making individual financial planning, individual financial policy has to be fixed then carefully select annuitization or self-annuitization to make the assess allocation optimization to protect old-age economic living no scruple.In this research, annuitization is categorized into fixed and variable annuities, while self-annuitization is categorized into saving account and stock investment. Amount the four categories, the future value of variable annuity and stock is uncertainty, but it matches the geometry Brownian motion stochastic model. Besides creating geometry Brownian motion model in order to simulate variable annuities and stocks, this research considered the effect of the mortality table and disability table as well as inflation factor in detail in order to make the simulation more precise. The stochastic geometry Brownian motion model for retirement financial planning was created and its solution applied with the random walk method. If the input factors changed, such as high interest, all others parameters will be changed, so the optimal assets distribution will be changed as well. Therefore, having the model and the program, all the possible condition will be solved.The simulation input parameters were the data of the present values of Taiwan. After simulation and discussion, the research has following important findings: stock was the best return investment tool between stock, saving account, variable annuities, and fixed annuities. So the higher percent of the stock, the higher return one can get but the risk is higher also. Once he/she got disability, the long-term care insurance did not fully cover his/her need when he/she was in a low- or middle-income. In the contrary, the higher-income did get a big help. The probability of ruin was affected by the following factors: the expect value of return, fluctuation, mortality table, disability table, basic consumption expense, inflation, and long-term care expense...etc. The key factors are the expect value of return and the basic consumption expense. The probability of ruin was negative proportion to the expect value of return, while the probability of ruin was positive proportion to the basic consumption expense. The time for occurring ruin would be taken place ahead of time when fluctuation was large but the probability of ruin was almost the same.Low- and middle-income retirements did not select variable annuities or fixed annuities only because their low liquidity. In spite of low- and middle-income, higher-income retirements should take more attention to the investment tool of stock markets which return was the best amount the four categories. The higher the percentage of stock he/she hold, the lower the probability of ruin he/she got and would get the better portfolio.It was not good to buy long-term care policies for those who were in low- and middle-income because it would accelerate to ruin. In the contrast, for those who were in higher-income, their assets deducted the long-term care expense was still enough to cover their living expenses. Hence, not only get more protection, but also exceed the long-term care expense which can be back to their account to get more money with compound interest. Therefore, the higher the long-term care policies (not exceed the critical value), the better protection they get.In low interest rate condition, the optimal portfolio for higher-income was the percentage of stock 85%, variable annuities, fixed annuities and saving account for 5% respectively. And when the long-term care policy was NT$1,000,000 then the probability of ruin almost approached to zero, but the asset expect value when die would increase to about 1.5 fold.