DC-type Pension Plan Study With Premium Return Terms

In recent years,with the development of capital market and population ageing problem increasingly prominent,defined-contribution pension(DC)plays a more and more important role in the social security system,at the same time,it is more and more popular in the pension fund market.In the accumulation phase,the premiums paid by the pension fund holders are determined in advance;after retirement,the income is related to the investment income of the pension wealth,of course,the risk of investment is also borne by the beneficiary.Therefore,it is very important for pension fund managers to study the optimal asset allocation strategy.In the cumulative phase,the premium return clause allows deceased pension fund holders to withdraw their premiums,thereby guaranteeing the rights of the deceased pension fund holders.So the DC pension scheme with the premium return clause is more in line with the actual situation.Therefore,its optimal investment strategy has become a research hotspot of scholars.This paper studies DC pension investment with premium return terms,which mainly works as follows:Firstly,because the premium return clause can guarantee the rights of the deceased pension fund holder,so the problem of defined-contribution(DC)pension with premium return is studied.Pensions are allowed to invest in a risk-free asset and a risky asset.Under HARA utility function,the explicit solution of optimal asset allocation strategy is obtained by using stochastic control theory and variable separation method;as special cases,the explicit solution of optimal asset allocation strategy under power utility function,logarithmic utility function and exponential utility function is derived.A numerical example is given to discuss and study the effect of premium return terms and important parameters on optimal asset allocation strategy under HARA utility function.Secondly,because the risks of inflation and volatility are the two most important factors affecting the pension plan,so the paper studies the problem of defined-contribution(DC)pension plan with premium return in the environment of inflation risk and fluctuation risk.The model assumes that the prices of risky asset are driven by Heston stochastic volatility model.Pensions are allowed to invest in a risk-free asset,a risky asset and an inflation-linked index bond.Under the mean-variance criterion,the explicit solution of the optimal investment strategy and effective frontier are obtained by using stochastic control theory,game theory and variable separation method.A numerical example is given to discuss and study the influence of the restitution clause on the optimal investment strategy and the influence of the nominal interest rate on the effective frontier.