随机通胀下基于终止风险的DB养老金计划的保费估值

The Premium Valuation of DB Pension Plan Based on Termination Risk Under Stochastic Inflation

针对随机通胀以及终止风险对DB养老金计划的养老金支付问题的影响,提出了在随机通胀的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;由于DB养老金计划可能发生两类终止而导致养老基金赤字和计划发起人公司破产而未能按照承诺支付养老金,就会产生支付缺口,此时,引入PBGC将缺口的养老金支付给养老金计划受益人。PBGC的引入能够充分保障受益人的利益,大大降低了受益人承担的风险。忽略通货膨胀会使结果有误差,因此,在随机通胀的基础上构建了基于两类终止风险的DB养老金计划的保费估值模型。最后,对模型进行了数值模拟。结果表明,通货膨胀的加入使得保费有所增加,虽然这一结果给计划发起人增加了负担,需要支付更多的保费给PBGC,但却降低了PBGC所承担的风险。该模型引入了随机通胀,使得研究的结果更符合实际。

In view of the impact of stochastic inflation and termination risk on DB Pension plan 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 inflation is proposed.Due to the possibility of two types of termination of DB pension plan,resulting in the pension fund deficit and the failure of the plan sponsor company to pay the pension as promised,a payment gap is generated.In this case,the PBGC is introduced to pay the pension plan beneficiary with the shortfall.The introduction of PBGC can fully protect the interests of beneficiaries and greatly reduce the risks borne by beneficiaries.Previous research has shown that ignoring inflation can skew the results.Therefore,based on stochastic inflation,the premium valuation model of DB pension plan based on two kinds of termination risks is constructed.Finally,the model is numerically simulated,and the results show that the addition of inflation increases the premium,which increases the burden on the initiators and requires them to pay more premiums to the PBGC,but reduces the risk borne by the PBGC.The model introduces stochastic inflation,which makes the research result more realistic.