Robust Optimal Policies For DC-type Pension Plans Under The Mean-variance Criterion

With the demographic transition and the evolution of the population dynamic mod-el of low birth rate and low death rate,the aging of population in many countries be-comes more and more prominent,which makes the pension fund management more and more important.In defined contribution(DC)pension plans,the contribution rate of participants is determined in advance and the investment risk is borne by the pension participants themselves,and the total pension accumulated during the payment phase is derived from the contributions in the pension plans and the investment returns from these contributions.Therefore,with the rapid development of the market economy,D-C pension plans have been more in line with the current state of pension management and play an important role in the social security systems of many countries.Obvious-ly,researching and solving DC pension plans with different investment environments has important theoretical and practical values.In the process of pension investment,investors are not only risk-averse,but also ambiguity-averse.Therefore,it is necessary to consider ambiguity-aversion in the investment problems.In addition,the goal of investors is to balance returns and risks,that is,to maximize fund investment returns while minimizing investment risks.The mean-variance model is just a double-objective optimization model to quantify the quantitative relationship between returns and risks.Therefore,this thesis mainly studies the robust optimal strategies of DC pension plans under the mean-variance criterion.The main contents are as follows:First of all,in order to get closer to the actual environment,we assume that both income level and stock price are driven by the Heston's stochastic volatility model,and establish a mean-variance model for a defined contribution(DC)pension plan.By us-ing the principle of stochastic dynamic programming and Lagrangian duality theorem,we obtain the explicit solutions for the efficient strategy and the efficient frontier.A numerical example shows the influence of income factors and volatility factors on the efficient strategy and the efficient frontier.Secondly,on the basis of the first content,we introduce ambiguity uncertainty and study the robust optimal investment problem under mean-variance criterion for an ambiguity-averse member(AAM).The member worries about model misspecification and aims to find robust optimal strategy.A continuous-time mean-variance model with ambiguity aversion for a DC pension plan is established.By using the Lagrangian multiplier method and stochastic optimal control theory,the explicit solutions for robust efficient strategy and efficient frontier are derived.In addition,some special cases are derived in detail.Finally,a numerical example is presented to illustrate the impact of model parameters on the robust efficient strategy and the efficient frontier,and some economic implications have been revealed.Thirdly,in the real environment,there are the sudden risk of the financial mar-ket and the death risk of pension members risks,so we introduce the jump-diffusion model here,and consider the return of premiums clauses in the DC pension plan.The robust time-consistent equilibrium strategy for mean-variance criterion with ambiguity aversion and the return of premiums clauses is further studied.By using the extended Hamilton-Jacobi-Bellman(HJB)equation,the robust time-consistent equilibrium strat-egy and the corresponding equilibrium value function are derived.In addition,some special cases are provided in detail.Finally,a numerical example illustrates the impact of model parameters on the robust equilibrium strategy and utility losses.