随机利率和死亡率下基于终止风险的DB养老金计划保费估值

Valuation of Premiums for DB Pension Plans Based on Termination Risk under Stochastic Interest Rate and Mortality Rate

针对随机利率和死亡率以及终止风险对DB养老金计划的养老金支付问题的影响,提出了在随机利率和死亡率条件下养老金福利担保公司(Pension Benefit Guaranty Corporation,PBGC)为基于提前终止和遇险终止风险的DB养老金计划提供担保的保费估值问题。假设养老基金投资于无风险金融资产和有风险金融资产,随机利率、死亡率以及养老基金和计划发起人资产均为随机过程;提出提前终止和遇险终止触发的条件,并建立在两种终止情况下的保费估值模型;最后通过数值模拟分析了随机利率和死亡率对保费的影响,并与Qian的保费进行比较;结果表明:随机利率和死亡率的引入使得保费相较于Qian的保费有所增加,虽然这一结果给计划发起人增加了负担,但是却降低了PBGC所承担的风险。

In view of the impact of stochastic interest rate and mortality rate and termination risk on DB Pension plan and Pension payment issues,the valuation of premium guaranteed by the Pension Benefit Guaranty Corporation(PBGC)for DB Pension plan based on the risk of premature termination and distress termination under stochastic interest rate and mortality rate is proposed.Assuming that pension funds invest in risk-free and risk financial assets,stochastic interest rate,mortality rate,and the assets of pension funds and plan sponsors are stochastic processes.The conditions of premature termination and distress termination trigger are proposed,and the premium valuation model is established under the two termination conditions.Finally,the impact of stochastic interest rate and mortality rate on premium is analyzed through numerical simulation,and the premium is compared with that of Qian.The result shows that the introduction of stochastic interest rate and mortality rate make the premium increase compared with Qian.Although this result increases the burden on the plan sponsor,it reduces the PBGC’s risk.