Abstract: For a long time, the choice of pension system has been the focus of theoretical and practical debate.Compared with single pension system, one of the purposes of introducing mixed pension system is to diversify risks. The main work of this paper is to study the optimal portfolio of different pension accounts from the perspective of risk and benefit.To this end, optimal account selection is analyzed first under deterministic conditions, then,a stochastic account revenue model is constructed.
In order to generate revenue scenarios of different accounts, mortality rate, fertility and return of assets are simulated based on Lee-Carter model, ARMA modeland CIR model, and thenthe classical Leslie population structure transition matrix is used to predict the change of population structure.On this basis, the revenuesof different pension accounts are calculated under different simulation scenarios.
Finally, the optimization technique is used to solve the portfolio model.The results show that:(1) the return of pay-as-you-gois negatively related to the return of funding, and the combination of the twosystems can form an effective risk hedging mechanism; (2) The efficient frontierof the mixed system is above the pay-as-you-go and funding, Therefore, from the risk-benefit perspective, mixed system is better than a single pension system; (3)Comparing with the optimalproportion of account,the current proportion of pay-as-you-go is higher, while the current proportion of the funding is low. The policy implication of this paper is that reducing the proportion of the current pay-as-you-go and increasing the proportion of funding can decrease the pension risks and increase income.

Key words: pension, pay-as-you-go, funding, portfolio theory