DC Pension Optimal Investment Problem For Hedging Liabilitie Based On Mortality Risk,Inflation Risk And Interest Rate Risk

Although China's pension insurance system has been gradually improved,it still faces great depreciation pressure due to the impact of inflation risk,mortality risk,interest rate risk and other risk factors as well as liabilities.This paper mainly studies the optimal investment ratio of DC type pension for hedging liabilities under the influence of non-systematic risks(such as mortality risk)and systematic risks(such as inflation risk and interest rate risk).The main content can be divided into the following parts:Firstly,this paper proposes the optimal investment ratio of DC pension based on mortality risk and stochastic inflation to hedge liabilities.It is assumed that members of the pension payment invest their pensions in the stock market and Banks,where mortality and inflation risk are independent.Inflation,earnings of investing stocks and Banks,member salaries and pension liabilities are all stochastic process,and mortality was predicted using the lee-carter model.Through the dynamic value equation of DC type pension for hedging liabilities under continuous time,the optimal model for minimizing the expected utility of pension wealth is established.The corresponding HJB equation is derived by combining stochastic control theory,and Legendre transformation method is used to obtain the optimal investment ratio of DC pension for hedging liabilities based on mortality and inflation risk.Finally,the numerical simulation analysis sh ows that the optimal investment ratio is more affected by inflation risk than mortality risk with the increase of investment duration.Secondly,considering the influence of consumption preference of DC pension investor,this paper studied the optimal investment ratio of DC pension with stochastic income and time-varying risk aversion coefficient,where inflation,stock returns,and wage processes are stochastic processes with interrelated geometric Brownian motions.Members of the pension payment invest pension in the stock market and Banks.Under the utility function with time-varying risk aversion coefficient and random income,we set up an optimization model to maximize the expected utility of wealth at the time of working and retirement,and solving the optimal investment ratio at the time of working and retirement respectively by using the Lagrange multiplier method.Then we analyze the influence of time-varying risk aversion coefficient on the optimal investment ratio.Finally,we summarize the research content of this paper,and point out some areas that need improvement and can be further expanded for future research.