Application Of Value At Risk Measurement Method In The Optimal Investment Strategy Of Defined Contribution Pension

Since stepping into the 21 st century,the aging of population is further deepening.The accompanying elderly care is becoming increasingly prominent.The pension system in China is a three-pillar pension security system.For the first pillar of basic old-age insurance,it’s basically covering the whole people.However,it’s faced up with many problems,such as heavy financial burden,low pension replacement rate and limited value added,etc.The third pillar commercial insurance was built up in June2017.However,it starts late.Furthermore,the development is slow and it is difficult to make effect in a short period of time.In this case,enterprise annuity should assume the second pillar of heavy responsibility,truly playing the role of supplementary pension insurance.Enterprise annuity is divided into DC(Defined Contribution)pension and DB(Defined Benefit)pension.In recent years,there are many countries which have moved from DB pension plan to DC pension plan,and DC pension plan has developed rapidly.The DC pension plan is also adopted in China.Therefore,it is particularly important for risk management of DC pensions.In this paper,Va R(Value-at-Risk)measurement method is used to carry on the risk management to the DC pension plan manager’s investment behavior.Under the situation of the economic recession,one-Va R constraint can lead to a greater loss of terminal wealth than the situation when Va R constraint is not taken into account.We use two Va R constraints to improve risk management and assume that there are only three types of financial assets,cash,bond and stock.Under two Va R constraints,fund managers choose the optimal investment strategy by maximizing the expected utility of the members’ terminal wealth of.We use a concave technique and Lagrange dual method to derive the optimal wealth process and optimal investment strategy.In addition,we makes a numerical analysis on the effects of Va R constraints and some model parameters on the distribution of optimal terminal wealth.We also makes a simulation analysis of the influence of Va R constraints on the initial investment strategy.Based on the theoretical and numerical results,we can conclude that two Va R constraints can significantly improve risk management in times of depression,which provides some reference for pension funds,government departments,regulators and investors in the aspect of quantitative risk management.