Assessment Of Premium For DB Pension Plan Based On Risk Under Stochastic Inflation And Stochastic Interest Rate

In the US,DB Pension plans are insured by the Pension Benefit Guaranty Corporation(PBGC).The PBGC provides financial support when the assets of pension funds and plan sponsors are unable to pay pensions.There are premature termination and distress termination in DB pension plan.This paper defines a critical value for the pension fund and the plan sponsor assets respectively.If the pension fund is lower than its critical value,the DB pension plan will premature termination.If the plan sponsor's assets fall below the threshold,the DB pension plan will distress termination.Aiming at the effects of stochastic inflation,stochastic interest rate,stochastic death rate and termination risk on the pension payment problem of DB pension plan,the premium valuation problem of PBGC guarantee for DB pension plan under the conditions of stochastic inflation,stochastic interest rate and stochastic mortality rate is proposed.First of all,there will be a payment gap due to the pension fund deficit caused by two types of termination of DB pension plan and the failure of plan sponsor's company to pay the pension as promised due to bankruptcy.In this case,PBGC will be introduced to pay the pension gap to the pension plan beneficiaries.The introduction of PBGC can fully protect the interests of the beneficiaries and greatly reduce the risks borne by the beneficiaries.Assuming that in DB pension plan,the pension fund invests in risk-free financial assets and risky financial assets.The assets of the pension fund and the plan sponsor are subject to random processes.The conditions of premature termination and distress termination are proposed,and the termination conditions are modeled by stop-time.Previous studies have shown that ignoring inflation can skew the results.Therefore,the premium valuation model of DB pension plan based on two termination risks constructed on the basis of stochastic inflation is more realistic.The numerical simulation of the model shows that the inflation increases the premium,which increases the burden on the plan sponsors and requires them to pay more premium to the PBGC,but reduces the risk borne by the PBGC.The model introduces stochastic inflation,which makes the research result more realistic.Then,due to the market fluctuations and the continuous decline of interest rates,the study of premium's issues on the basis of fixed interest rates is not consistent with the reality.Therefore,the follow-up research of this paper is completed under the condition of stochastic interest rates.The premium valuation models under stochastic inflation and stochastic interest rate and stochastic interest rate and stochastic mortality rate are constructed respectively.The numerical simulation of these two models shows that the addition of inflation,stochastic interest rate and mortality rate will increase the insurance premium.Finally,the research results obtained in this paper are summarized and the paper is given.