Research On The Models Of Investment Portfolio Of DC Pension Funds Based On PJD Process

The portfolio problem of Defined Contribution pension is always one of the important issues in research field of portfolio.In the modern financial market,the DC pension fund managers often have to face three main factors: inflation,stochastic interest rates and short selling constraints.Therefore,fund managers must rationally choose portfolios based on these factors.The experience of modern financial practice shows that the violent change in the price of risk assets is increasingly frequent,which brings great loss to the economy based on DC pension fund in reality.Therefore,in the current research on portfolio of DC pension fund,it is more important to consider the impact of sharp changes in risk asset prices on portfolio.Accordingly,on the basis of the existing research,we take the portfolio of DC pension fund as the research object.Under the constraints of three major factors,such as inflation,random interest rate and short selling constraint,which affect the choice of portfolio,modeling and analyzing the risk asset price process with Poisson jump diffusion process.Stochastic analysis theory,stochastic control theory and fuzzy random theory are used to discuss the portfolio of DC pension fund based on the PJD process under the constraints of three typical financial markets,which are inflation,random stochastic rates and market short selling constraints.Firstly,in view of the important characteristic that inflation affects investor's investment behavior in the modern financial market,makes a hypothesis that inflation subject to geometric Brown movement and aims at maximizing the discounted expected utility of terminal wealth inflation,and uses stochastic control theory and fuzzy random theory to obtain the portfolio of DC pension fund managers under the condition of inflation.Analyzing the numerical simulation results,it is found that the jump intensity will become one of the factors affecting the optimal investment of risk assets when the impact of the financial market jump events on the portfolio is considered.In the case of random inflation constraints,the optimal investment of risk assets with the increase of the inflation volatility presents a trend of increasing first and then decreasing.Furthermore,using the fuzzy random theory,the jump intensity ? of financial market jump event is pasting,and modeled a triangular fuzzy number to the right deviation,under the logarithmic utility function,the optimal investment interval of the DC pension fund manager is obtained.With the increasing improvement of the subjective judgment reliability of the DC pension fund managers,the investment interval of the fund managers in the risk assets and the riskless assets will gradually narrow until the optimal investment and the optimal investment of the riskless assets become a definite real number and lose the ambiguity.Secondly,according to the random characteristics of the risk-free interest rate in the modern financial market,the risk-free interest rate is randomized and aims at maximizing the expected utility of the terminal wealth,and the stochastic control technology and fuzzy random analysis are used to obtain the portfolio of the DC pension fund under the random interest rate condition.After analyzing the results of the numerical simulation and considering the random interest rate situation and the jump of stock price,the effect of risk aversion on optimal investment is considered.The stock investment will decrease with the increase of investor risk aversion coefficient ?,The bond investment increases with the risk aversion factor ? of the investor,the investment in bank deposits decreases with the increase of investor risk aversion factor ?.Considering the effect of investment term on the optimal investment,it is found that with the increase of investment period,the stock investment is unchanged,and the bond will show an increasing trend of gradually decreasing slope,and the trend of bank deposit investment is just opposite to the bond investment trend.When considering the impact of jump intensity on the optimal investment,it is found that the bond investment does not change with the increasing of the jump intensity ?,and the stock investment tends to decrease,and the trend of the bank deposit investment is opposite to the stock investment trend.Furthermore,using the fuzzy random theory,the jump intensity ? of the financial market jump event is pasting,and a triangular fuzzy number to the right deviation is formed.Under the logarithmic utility function,the optimal investment interval of the DC type pension fund manager is obtained.With the increasing improvement of the subjective judgment reliability of the DC pension fund managers,the investment interval of the fund managers in the bank deposits,bonds and stocks will gradually narrow,until the optimal investment of bank deposits,bonds and stocks becomes a definite real number,and the ambiguity is lost.Finally,considering the short selling constraints in the modern financial market,the short selling constraint of the financial market is taken into account.The mean-variance model is constructed with the LQ method under the classical continuous time mean-variance optimal portfolio analysis framework.Then,the initial mean-variance model asset portfolio problem is converted to the auxiliary mean-variance model.Due to the existence of short selling constraints,the traditional maximum value method and martingale method cannot be applied directly.Considering the validity of the viscous solution theory in the problem of stochastic LQ with non-negative constraints,the theory of viscous solution is used to describe the optimal portfolio problem,and then the optimal solution and effective frontier of the effective most investment are obtained.The results show that the risk asset price jump will affect the effective optimal investment and the effective frontier after considering the jump in the price of risk asset.And,it's similar to the past research that does not consider the risk asset price jump and only consider the diffusion problem,if the DC pension fund manager's wealth is large enough,the fund manager's investment in the venture capital will be kept to zero because of the short selling constraint,and all the assets will be invested in the riskless assets.In a word,in the DC pension fund portfolio management problem,we takes into account the three main factors that affect the portfolio selection in the financial market: inflation,random interest rate and short selling constraint,and fully consider the jump characteristics of the risk asset price,and study the portfolio of DC pension fund.The research is more in line with the portfolio selection process of the current financial market DC pension fund.It also provides a reference model and method for the management of the market related pension fund managers,which has high theoretical and practical significance.At the same time,as China's pension fund gradually enters the capital market,the research results provide some reference for the investment decision making of China's pension fund into the market.