Robust Mean-variance Strategy For DC Pension Funds Under Multiple Risk Environment

As people’s life expectancy is getting longer and the fertility rate is getting lower and lower,pension fund management problem has become the hot spot of the industry’s most concern.As one of the main types of pension plans,the defined contribution(DC)pension has the advantage of alleviating the pressure on the social security system.In the DC pension plan,the contribution rate is determined,and the pension payment depends on the contribution and investment income during the period before retirement.Because the drift parameters are difficult to accurately estimate,and lack of the information of the probability measure,the real probability measure has ambiguity(model uncertainty).In this case,the decision maker hopes to find a more robust optimal investment strategy to deal with the worst case that may occur due to the deviation of the reference measurement from the true measurement.Therefore,this paper first considers the optimal investment strategy of DC pensions under the framework of stochastic interest rate and stochastic volatility under the mean-variance criterion.Secondly,on this basis,the impact of ambiguity on the optimal asset allocation of DC pension plans is studied.The main research work is as follows:First of all,under the mean-variance criterion,the optimal investment strategy for DC pensions including interest rate risk,volatility risk,and salary risk is considered.In the pension accumulation stage,the interest rate level,volatility level,and salary level are considered to be stochastic,and it is assumed that the term structure of interest rate meets the stochastic affine interest rate model,and the stock price volatility meets the Heston stochastic volatility model.By using the principle of stochastic dynamic programming and Lagrangian duality theorem,we obtain the explicit solutions for the efficient strategy and the efficient frontier.Research results show that the capital market line with interest rate risk,volatility risk and salary risk environments is still a straight line in a mean-standard deviation plane,and the efficient strategy only depends on both instantaneous interest rate level and instantaneous salary level.Secondly,on the basis of the above content,we study the robust optimal investment problem of DC pensions with an ambiguity-averse member(AAM)under the mean-variance criterion,which considers multiple risks.The financial market consists of a risk-free asset,a risky asset and a rolling bond.We assume that the term structure of interest rate is driven by an affine interest rate model,while the stock price and the salary level are modeled by a stochastic volatility model with stochastic interest rate.The goal of an AAM is to find a robust optimal strategy to maximize the expectation terminal wealth and minimize the variance of terminal wealth in the worst-case scenario.By applying the Lagrange dual theory and the stochastic dynamic programming approach,we obtain the closed-form expressions of the robust efficient strategy and the efficient frontier.Finally,a numerical example is used to illustrate the influence of some parameters on the robust efficient strategy and the efficient frontier.The results show that the more ambiguity averse the AAM is,the more conservative the investment strategy adopted.