Research On DC Pension Plan Considering Random Interest Rate And Random Salary Under The Mean-variance Criterion

With the evolution of population and the development of economic market,the investment problem of determining the contribution(DC)type pension has become an important research topic in the current pension plan.In the DC pension scheme,the rate of contribution is determined,and the level of payment by the pension fund depends on contributions up to the pre-retirement period and the investment income from these contributions.It is of great practical significance to study and solve the optimal investment strategy of pension in different environments,which not only enrich and develop pension investment theory,but also provide investment basis for fund managers in the process of investment.Interest rates and random salary are the most direct and important factors that affect the ability to pay for pensions,and they all vary randomly.In the investment process,the goal of the fund manager is to find an optimal investment strategy to minimize the investment risk when maximizing the investment return.The mean-variance model can quantitatively describe the relationship between investment return and risk.Therefore,this essay studies and analyzes the DC pension scheme with random interest rate and random salary under the mean-variance criterion.The main contents are as follows:First,assuming that the interest rate term structure satisfies the cox-ingersoll-ross(CIR)interest rate model,the fund manager considers investing the pension in a financial market consisting of a risk-free asset,multiple stocks,and a zero coupon bond in order to maintain and increase the value of the pension.Aiming at the expectations of fund managers,We establish a mean-variance model of the cumulative stage defined contribution(DC)pension scheme,and obtain the explicit solution of effective strategy and effective frontier by the principle of stochastic dynamic programming and Lagrange dual theorem.The results show that the capital market line in the stochastic interest rate environment is still a straight line in the mean-standard deviation plane.Moreover the effective strategy is directly related to the instantaneous interest rate level,and the effective boundary is not directly dependent on the instantaneous interest rate level.Second,based on the first part of the study,considering the variable random salary we study the optimal investment of DC pension with random interest rate andrandom salary under the mean-variance criterion.Firstly,we assume that the interest rate structure satisfies the affine interest rate model,and the financial market consists of a risk-free asset,a risky asset,and a zero-interest bond.Secondly,in order to achieve the goal expected by fund managers,we set up the mean-variance model of the accumulated stage pension,and apply the principle of stochastic dynamic programming and Lagrange dual theorem to get the explicit solution of the effective strategy and the effective boundary.Finally,we perform the numerical analyse of fixing some parameters,and explain the corresponding economic meaning.The results show that both interest rate and random salary have great influence on effective strategy and effective boundary.