A Study On Risk Management Of DB Pension Plan Under Random Inflation

Considering the risk factors in DB pension plan:systemic risk,longevity risk,investment risk,inflation risk and default risk.In order to study the risk management of DB pension plans,this paper proposes three options—funding options,buyout options and surrender options,analyzes the impact of funding options,buyout options and surrender options on risk management of these three options,and gives how to determine the price of these three options and the optimal surrender time of the options.Moreover,this paper also studies the optimal investment strategy of the target benefit pension plans of DB pension and DC pension combination.Firstly,considering the risks borne DB pension sponsors,namely systemic risk,longevity risk,inflation risk and investment risk,two options which are the DB pension fund option(funding option)and DB pension acquisition option(buyout option)are proposed.When they reach a certain level,funding option and buyout option provide funds for the under-funded and the well-funded programs to cover acquisition risk premiums and pension fund deficits.In order to increase the liquidity of the market,a transparent DB pension fund index is created to determine the return of options,calculated on the basis of the observed capital market index,the publicly available mortality table and the mandatory contribution of DB pensions.The evolution of the DB pension fund index is modeled as the ratio of the DB pension assets index to the DB pension liability index.The DB pension assets index is calculated from the three market indexes:the S&P 500,the Merrill Lynch Bond Index and the three-month Treasury bond index,based on the pre-determined investment weight.While the DB pension liability index is assessed by an available publicly predicted mortality table,which is counted by Lee and Carter mortality models.A simulation based on the pricing framework is then introduced to determine the price of the proposed DB pension option.And then the results are numerically analyzed.The analysis shows that these options are effective and affordable when the funds are sufficient and insufficient.Sensitivity analysis also shows that our pricing model is reliability and may provide more effective options for DB pension plan sponsors.Secondly,according to the systemic risk and default risk that policyholders encounter in the process of insurance,the optimal surrender strategy of DB pension plan based on random inflation risk is studied.The scheme has a minimum protection function,and policy holders can exercise surrender options at any time.In order to find the best time to exercise surrender option,the optimal surrender time of DB annuity plan with surrender option is transformed into a free boundary problem.From this,a corresponding nonhomogeneous partial differential equation can be obtained.After the integral transformation of the nonhomogeneous partial differential equation is carried out by using Merlin transformation,the integral equation is solved by RIM recurrence integration method,and an integral equation and the optimal exit boundary of surrender option estimation are obtained.The research shows that this option provides more protection for the policy holder and makes the policy holder to have more options.In addition,we give the nature of the fair charge rate and analyze the influence of different investment ratios on account value and derive the optimal surrender time by numerical simulation.In addition,the optimal investment strategy based on random mortality,random inflation and intergenerational risk is also studied,which is a combination of DB and DC pension schemes.Using the stochastic optimal control method,based on the intergenerational risk and inflation risk,the optimal investment strategy of the target benefit pension plans is investigated on the basis of measuring the random wage rate under the random mortality rate and the inflation risk of personnel in the plan and the correlation between wage changes and financial market fluctuations.The optimal investment strategy and the optimal income adjustment strategy of the target benefit pension are given.The research shows that the financial market parameters and wage rate can significantly impact the optimal investment strategy.Finally,the research results obtained in this paper are summarized and the paper is given.