Research On The Optimal Investment Of DC-type Corporate Annuities With Default Bonds Under Inflation

Since the reform and opening up,China's old-age security system has been gradually established and improved,but the ageing of our population has continued to intensify,and the old-age dependency ratio has risen rapidly,resulting in a growing gap in the income and expenditure of basic pension insurance,the first pillar of our old-age security system.As the third pillar of personal savings-type pension insurance is still in its infancy,therefore,giving full play to the role of the second pillar of enterprise annuity has become one of the important countermeasures for China's current pension problem.Asset allocation,as the core of the long-term investment income of the enterprise annuity,will have a direct impact on the accumulated balance of the annuity plan.Therefore,optimizing the allocation of enterprise annuity assets is of great significance to the operation of current enterprise annuities.At present,the applicability and universal use of DC-type enterprise annuities are relatively high in China.Many scholars have researched the optimal investment strategies of DC-type enterprise annuities.In these studies,only the defaulted bonds or only the inflation factor has been considered.Few studies have considered both defaulted bonds and inflation factors,and less research has been conducted on optimal investment strategies for corporate annuities at random interest rates.Therefore,this paper considers both the inflation factor and the default bonds,and conducts research on the optimal investment strategy of DCtype enterprise annuities at fixed and random interest rates,respectively.Because the investment term of corporate annuities is relatively long,this article considers the impact of inflation on investment strategies.Due to the frequent occurrence of bond default events in recent years,this paper introduces default bonds when constructing wealth portfolios,and studies the optimal investment strategy of DCtype corporate annuities with default bonds under inflation.This paper first obtains the optimal asset allocation model under fixed and random interest rates based on portfolio theory,and obtains the fully nonlinear partial differential HJB equation corresponding to the optimal asset allocation model based on stochastic control theory.The equation is applied to the equation using HJB variation method The separation of variables is transformed into a linear ordinary differential equation,and the explicit solution of the optimal investment strategy is obtained by solving the ordinary differential equation,which greatly reduces the calculation amount in the process of obtaining the numerical solution by the interpolation algorithm,and increases the calculation speed.Secondly,the optimal investment strategy obtained is numerically simulated.Through the sensitivity analysis of the parameters,it is found that with the remaining variables remaining unchanged,as the inflation rate or inflation volatility increases,the proportion of risk assets investment increases first and then decrease;the proportion of investment in defaultable bonds increases with increasing credit spreads,and decreases with increasing volatility or intensity of default,while the investment ratio of non-defaulting bonds and defaultable bonds shows a growing and decreasing relationship.Finally,this paper conducts an empirical analysis of the optimal investment strategy for DC-type enterprise annuities at a fixed interest rate,performs parameter estimation on the data from 2010-2017,and uses the estimated parameters to predict the monthly return rate and annual rate of the strategy in 2018-2019.Compared with the corresponding returns of the broader market,it is found that the returns of the strategy in this paper are relatively high,so as to verify the effectiveness of this strategy.