Research On Optimal Investment Strategies Under Two Stochastic Models For DC Pension

With the continuous improvement of modern medical level,the number of elderly people in the world is also increasing,and the pension problem is concerned by the government.The value-added and preservation of pension funds is achieved through optimal investment.In this regard,the core problem of DC pension management is to find its optimal investment strategy so that the expected utility of all funds in the account can be maximized at the moment of retirement.In the actual financial market,the market price of interest rates and risks change over time,that is to say,they all fluctuate randomly.Therefore,it is of great practical significance to research on the optimal investment strategy for DC type old-age pension when the market price of risk and the interest rate fluctuate randomly.This paper studies the optimal portfolio of maximizing all funds in the accounts of DC pension participants in retirement under two types of stochastic models.Firstly,this paper studies the optimal investment strategy under the affine-form square-root stochastic model for DC type old-age pension.Suppose that the monetary market contains a risk asset and a risk-free asset.By using the stochastic control theory and solving the homologous HJB equation,the analysis formula of the optimal value function and the optimal investment strategy with CRRA and CARA utility are acquired respectively.Then,we analyze the influence of factors such as random factor,drift rate of risky asset and period in the monetary market on the optimal portfolio solution with CRRA utility.Secondly,this paper studies the optimal investment strategy under affine interest rate stochastic model for DC type old-age pension.It is assumed that the monetary market contains a kind of risk-free asset,a kind of risk asset and a kind of zero-coupon bond.Using stochastic control theory and Legendre transformation-dual theory,the analysis formula of the optimal value function and the optimal portfolio solution with HARA and CARA utility are acquired respectively by solving HJB equations.And the impact of major parameters such as the payment rate and stock volatility in the financial market under the HARA utility on the optimal investment strategy are explained.