An Optimal Asset Allocation Problem Of DC Pension Under Incomplete Market And Stochastic Interest Rate Model

With the rapid development of market economy and medical treatment,the number of elderly people is increasing,and the social population structure gradually aging,which makes the national pension insurance system face great challenges.Nowadays,the market of endowment insurance products emerge endlessly,how to choose the appropriate pension insurance has attracted attention of all.People buy pension insurance to hope that they can get more pension from pension accounts while taking lower risks.So pension managers should think about how to find the right investment strategy to maximize the final income or minimize the bankruptcy probability of pension.This thesis mainly studies the optimal resource allocation problem of DC pension under the constraint of minimum income guarantee.With the goal of maximizing the expected utility of pension terminal wealth,the minimum maximum martingale measure method is used to solve the optimal strategy.This thesis is divided into two parts,in the first part,based on the forward interest rate model,DC pension is invested in risk-free assets,nominal zero-coupon bonds,inflation-indexed bonds and stocks in incomplete market.By constructing self-financing portfolio,the optimal strategies of pension under logarithmic utility function and exponential utility function are obtained respectively.The second part constructs the financial market based on the jump diffusion forward interest rate model,considers the minimum return guarantee related to inflation,and obtains the optimal strategy under the logarithmic utility function.